Permission-based multiple access communications systems

ABSTRACT

Systems ( 100 ) and methods ( 400 ) for selectively controlling access to multiple data streams which are communicated using a shared frequency spectrum and shared spreading codes. The methods involve generating a first product signal (FPS) by spreading first symbols of a first amplitude modulated (AM) signal using a first spreading code (SC). The methods also involve generating a second product signal (SPS) by spreading second symbols of a complimentary AM signal using a second SC. The FPS ( 124 ) and SPS  126  are combined to form a protected data communication signal (PDCS) including first data recoverable by a receiver ( 106 ). A global data communication signal (GDCS) is combined with PDCS ( 128 ) to form an output signal ( 140 ) having a spread spectrum format. The GDCS is generated using a digital modulation process and includes second data recoverable by a plurality of receivers ( 106, 108 ).

BACKGROUND OF THE INVENTION

1. Statement of the Technical Field

The invention concerns communications systems. More particularly, theinvention concerns communications systems employing permission-basedchaos-based multiple access methods.

2. Description of the Related Art

Pseudorandom number generators (PRNG) generally utilize digital logic ora digital computer and one or more algorithms to generate a sequence ofnumbers. While the output of conventional PRNG may approximate some ofthe properties of random numbers, they are not truly random. Forexample, the output of a PRNG has cyclostationary features that can beidentified by analytical processes.

Chaotic systems can generally be thought of as systems which varyunpredictably unless all of its properties are known. When measured orobserved, chaotic systems do not reveal any discernible regularity ororder. Chaotic systems are distinguished by a sensitive dependence on aset of initial conditions and by having an evolution through time andspace that appears to be quite random. However, despite its “random”appearance, chaos is a deterministic evolution.

Practically speaking, chaotic signals are extracted from chaotic systemsand have random-like, non-periodic properties that are generateddeterministically and are distinguishable from pseudo-random signalsgenerated using conventional PRNG devices. In general, a chaoticsequence is one in which the sequence is empirically indistinguishablefrom true randomness absent some knowledge regarding the algorithm whichis generating the chaos.

Some have proposed the use of multiple pseudo-random number generatorsto generate a digital chaotic-like sequence. However, such systems onlyproduce more complex pseudo-random number sequences that possess allpseudo-random artifacts and no chaotic properties. While certainpolynomials can generate chaotic behavior, it is commonly held thatarithmetic required to generate chaotic number sequences requires animpractical implementation due to the precisions required.

Communications systems utilizing chaotic sequences offer promise forbeing the basis of a next generation of low probability of intercept(LPI) waveforms, low probability of detection (LPD) waveforms, andsecure waveforms. While many such communications systems have beendeveloped for generating chaotically modulated waveforms, suchcommunications systems suffer from low throughput. The term“throughput”, as used herein, refers to the amount of data transmittedover a data link during a specific amount of time. This throughputlimitation stems from the fact that a chaotic signal is produced bymeans of a chaotic analog circuit subject to drift.

The throughput limitation with chaos based communication systems can betraced to the way in which chaos generators have been implemented. Chaosgenerators have been conventionally constructed using analog chaoticcircuits. The reason for reliance on analog circuits for this task hasbeen the widely held conventional belief that efficient digitalgeneration of chaos is impossible. Notwithstanding the apparentnecessity of using analog type chaos generators, that approach has notbeen without problems. For example, analog chaos generator circuits areknown to drift over time. The term “drift”, as used herein, refers to aslow long term variation in one or more parameters of a circuit. Theproblem with such analog circuits is that the inherent drift forces therequirement that state information must be constantly transferred over acommunication channel to keep a transmitter and receiver synchronized.

The transmitter and receiver in coherent chaos based communicationsystems are synchronized by exchanging state information over a datalink. Such a synchronization process offers diminishing return becausestate information must be exchanged more often between the transmitterand the receiver to obtain a high data rate. This high data rate resultsin a faster relative drift. In effect, state information must beexchanged at an increased rate between the transmitter and receiver tocounteract the faster relative drift. Although some analog chaoticcommunications systems employ a relatively efficient synchronizationprocess, these chaotic communications systems still suffer from lowthroughput.

The alternative to date has been to implement non-coherent chaoticwaveforms. However, non-coherent waveform based communication systemssuffer from reduced throughput, error rate performance, andexploitability. In this context, the phrase “non-coherent waveform”means that the receiver is not required to reproduce any synchronizedcopy of the chaotic signals that have been generated in the transmitter.The phrase “communications using a coherent waveform” means that thereceiver is required to reproduce a synchronized copy of the chaoticsignals that have been generated in the transmitter.

In view of the forgoing, there is a need for a coherent chaos-basedcommunications system having an increased throughput. There is also aneed for a chaos-based communications system configured for generating asignal having chaotic properties. As such, there is further a need for achaos-based communications system that corrects drift between atransmitter and a receiver without an extreme compromise of throughput.Further, there is a need for a secure communication system that providespermission-based segmentation of transmitted data to multiple usergroups.

SUMMARY OF THE INVENTION

Embodiments of the present invention relate to methods for selectivelycontrolling access to multiple data streams which are communicated usinga shared frequency spectrum and shared spreading codes. The methodsinvolve generating a first product signal by spreading first symbols ofa first amplitude modulated signal using a first spreading code. Themethods also involve generating a second product signal by spreadingsecond symbols of a complimentary amplitude modulated signal using asecond spreading code. The first and second spreading codes includepseudo-random number sequences and/or digitally generated chaoticsequences. The second spreading code is orthogonal or statisticallyorthogonal to the first spreading code.

The first and second product signals are combined to form a protecteddata communication signal. The protected data communication signalincludes first data recoverable by at least one receiver of a pluralityof receivers. The methods further involve combining a global datacommunication signal and the protected data communication signal to forman output signal having a spread spectrum format. The global datacommunication signal is generated using a digital modulation process.The digital modulation process can include a phase modulation process.The global data communication signal includes second data recoverable byall of the receivers.

According to an aspect of the present invention, the first and secondproduct signals are additively combined to produce a constant powerenvelope protected data communication signal. The global datacommunication signal is recovered at a first receiver of the pluralityof receivers by de-spreading the output signal using a sum of a thirdspreading code and a fourth spreading code which are respectivelyidentical to the first spreading code and the second spreading code. Thefirst and third spreading codes are synchronized in time. Also, thesecond and fourth spreading codes are synchronized in time. Notably, thefirst receiver is prevented from independently recovering the thirdspreading code or the fourth spreading code. The first product signal isrecovered at the first or a second receiver of the plurality ofreceivers by de-spreading the output using a third spreading code thatis identical to the first spreading code.

Embodiments of the present invention also relate to communicationsystems configured for selectively controlling access to multiple datastreams which are communicated using a shared frequency spectrum andshared spreading codes. The communication systems comprise a firstdiscrete time amplitude modulator, a second discrete time amplitudemodulator, a first combiner, and a second combiner. The first discretetime amplitude modulator is configured for generating a first productsignal by spreading first symbols of a first amplitude modulated signalusing a first spreading code. The second discrete time amplitudemodulator is configured for generating a second product signal byspreading second symbols of a complimentary amplitude modulated signalusing a second spreading code. The first combiner is configured forcombining the first and second product signals to form a protected datacommunication signal. The protected data signal includes first datarecoverable by at least one receiver of a plurality of receivers. Thesecond combiner is configured for combining a global data communicationsignal and the protected data communication signal to form an outputsignal having a spread spectrum format. The global data communicationsignal is generated using a digital modulation process. The global datacommunication signal includes second data recoverable by all of thereceivers.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will be described with reference to the following drawingfigures, in which like numerals represent like items throughout thefigures, and in which:

FIG. 1A is a schematic illustration of an exemplary multiple accesscommunication system that is useful for understanding the invention.

FIG. 1B is a schematic illustration of exemplary symbol constellationsthat are useful for understanding the invention.

FIG. 2A is a conceptual diagram of a method for removing cyclostationaryand statistical artifacts from a pulse amplitude modulated (PAM) signalthat is useful for understanding the present invention.

FIG. 2B is a schematic illustration of an amplitude adjustment processthat is useful for understanding the present invention.

FIG. 2C is a schematic illustration of an improved amplitude adjustmentprocess that is useful for understanding the present invention.

FIG. 3 is a schematic illustration of a signal separation that is usefulfor understanding the present invention.

FIG. 4 is a flow diagram of a method for generating a chaotic amplitudemodulated signal absent of statistical artifacts and having separablesignal components.

FIG. 5 is a block diagram of a chaotic pulse amplitude modulation (CPAM)system used in construction of the protected data communication signalaccording to an embodiment of the invention.

FIG. 6 is a more detailed block diagram of the transmitter shown in FIG.1A according to an embodiment of the present invention.

FIG. 7A is a more detailed block diagram of the full permission receivershown in FIG. 1A according to an embodiment of the invention.

FIG. 7B is a more detailed block diagram of the full permission receivershown in FIG. 1A according to an embodiment of the invention.

FIG. 8A is a more detailed block diagram of the partial permissionreceiver shown in FIG. 1A according to an embodiment of the invention.

FIG. 8B is a more detailed block diagram of the partial permissionreceiver shown in FIG. 1A according to an embodiment of the invention.

FIG. 9 is a conceptual diagram of the chaos generators of FIGS. 6, 7Band 8B.

FIG. 10 is a flow diagram of a method for generating a chaotic spreadingcode (or chaotic sequence) according to an embodiment of the invention.

FIG. 11 is a block diagram of a chaos generator shown in FIG. 6according to an embodiment of the invention.

DETAILED DESCRIPTION

Embodiments of the present invention will now be described with respectto FIGS. 1A-11. Embodiments of the present invention relate topermission-based multiple access communications systems. Multiple accesscommunications systems according to embodiments of the present inventiongenerally allow multiple signals to be transmitted from a plurality ofsources at the same time over the same frequency band using distinctspreading codes. The multiple access communications described herein areaccomplished using orthogonal or statistically orthogonal spreadingcodes in access unique configurations to spread each signal over alarge, common frequency band. The orthogonal or statistically orthogonalspreading codes advantageously include distinct chaotic spreading codesgenerated by chaos generators. Appropriate orthogonal or statisticallyorthogonal spreading codes in unique configurations are used at one ormore receivers to recover the data signals intended for a particularuser. In effect, the communications system allows users with certainkeys to access protected data (e.g., data targeted to specific users)and/or global data (e.g., data targeted to all authorized users). Theterm statistically orthogonal spreading codes as used herein refers tospreading codes with whose inner product over a finite duration has astatistical expectation of zero.

The communications systems described herein can be utilized in a varietyof different applications where access to certain types of data isselectively controlled. The use of unique configurations of the samespreading codes can be coupled with the use of multiple spreading codesto expand the number of unique access permissions. Such applicationsinclude, but are not limited to, military applications and commercialmobile/cellular telephone applications.

Permission Based Multiple Access Communications System

Referring now to FIG. 1A, there is provided a schematic illustration ofan exemplary permission based multiple access communication system(PBMACS) 100 according to an embodiment of the invention. As shown inFIG. 1A, PBMACS 100 is comprised of a transmitter 102 and receivers 106,108. Transmitter 102 is generally configured to generate an outputcommunication signal (OCS) 140 having chaotic properties. OCS 140 caninclude protected data (e.g., data targeted to specific users) and/orglobal data (e.g., data targeted to all authorized users). OCS 140 isgenerated using a coherent chaotic sequence spread spectrum (CCSSS)method.

The global data communication signal 134 is formed using a quadraturephase and amplitude modulation (e.g. QAM, APSK) such that global data isencoded in both the phase and amplitude of the global data communicationsignal 134. In embodiments of the present invention, the global datacommunication signal 134 is in effect formed using phase modulationonly, by selecting a constant amplitude phase-modulated complex valuefor the duration of a global data symbol. The phase is exclusive toglobal data. One embodiment of forming the global data signal is asfollows. A first global data signal (not shown) is formed by combiningglobal data symbols (e.g., quadrature amplitude shift keying symbols) ofa punctured quadrature amplitude modulated (PQAM) constellation with afixed and specific amplitude.

In contrast to the global data communication signal 134 which is formedeffectively using phase modulation only, a protected data communicationsignal 128 is formed using a combination of pulse amplitude modulated(PAM) symbols and the amplitude complements of the symbols. A firstproduct signal 124 is formed by combining protected data symbols (e.g.,PAM symbols) of a first amplitude modulated signal 120 with a firstchaotic spreading code CSC₁. A second product signal 126 is formed bycombining protected data symbols (e.g., PAM symbols) of a secondamplitude modulated signal 122 with a second chaotic spreading codeCSC₂. Chaotic spreading code CSC₂ is advantageously selected so that itis orthogonal or statistically orthogonal with respect to the chaoticspreading code CSC₁. The second amplitude modulated signal 122 hassymbol amplitudes which are the complements of the amplitude of theamplitude modulated signal 120. The chaotic spreading codes CSC₁, CSC₂spread the spectrum of the respective data symbols according to aspreading ratio.

A protected data communication signal 128 is obtained by combining thefirst product signal 124 with the second product signal 126. Theprotected data communication signal 128 is then combined with the globaldata communication signal 134 to generate the OCS 140. The protecteddata communication signal acts to spread the spectrum of the respectiveglobal data symbols according to a spreading ratio.

Transmitter 102 is also configured to transmit the OCS 140 to thereceivers 106, 108. OCS 140 can be transmitted from the transmitter 102over the communications channel 104. An embodiment of transmitter 102will be described below in relation to FIG. 6.

Referring now to FIG. 1B, there is provided a schematic illustration ofan exemplary punctured quadrature amplitude modulated constellation.Shown in FIG. 1B is a 64 quadrature amplitude modulation (QAM)constellation 150, a punctured QAM constellation with twelve (12)allowed symbols 152, the 4 symbols in the punctured QAM constellationthat comprise the QPSK symbols in one embodiment of the global data 154,and the 4 symbols and their complementary symbols which comprise oneembodiment of the protected data 156 symbols after combination with aQPSK reduction of the global data signal. As seen in the punctured QAMconstellation 152, all allowed constellation values lie on two axes. Asseen in constellations 152, 154, 156, the amplitudes of the protectedsymbols and the amplitudes of the complementary protected symbolsallowed on the constellations are symmetric about the amplitudes allowedfor the global data symbols.

Referring again to FIG. 1A, receiver 106 is generally configured forreceiving signals transmitted from the transmitter 102. Receiver 106 isa full permission receiver. The phrase “full permission receiver”, asused herein, means that the receiver is configured to access theprotected data and the global data. The global data is recovered bycorrelating the OCS 140 with a first de-spreading code. The firstde-spreading code is a chaotic sequence defined by the mathematicalexpression DSC=CSC₁′+CSC₂′. Receiver 106 is configured to generate areplica of the first chaotic spreading code CSC₁ and a replica of thesecond chaotic spreading code CSC₂. For convenience, these shall bereferred to herein as CSC₁′ and CSC₂′. Each of the replica spreadingcodes CSC₁′, CSC₂′ is synchronized in time and frequency with therespective chaotic spreading code CSC₁, CSC₂. The PAM signal withprotected data 120 and the complementary PAM signal with protected data122 are recovered by correlating the OCS 140 with CSC₁′ and CSC₂′,respectively. Each of these correlations are performed independently forthe recovery of the protected data. An exemplary embodiment of thereceiver 106 will be described below in relation to FIG. 7.

Receiver 108 is generally configured for receiving signals transmittedfrom the transmitter 102. However, receiver 108 is a partial permissionreceiver. The phrase “partial permission receiver”, as used herein,means that the receiver is configured to only access global data. Theglobal data is recovered by correlating the OCS 140 with a de-spreadingcode. The de-spreading code is a chaotic sequence defined by themathematical expression DSC=CSC₁′+CSC₂′. In this regard, it should beunderstood that receiver 108 is configured to generate a replica of thesum of the first chaotic spreading code CSC₁ and the second chaoticspreading code CSC₂. As noted, these replica chaotic spreading codes arereferred to as herein as CSC₁′ and CSC₂′. The replica spreading codesCSC₁′, CSC₂′ are synchronized in time and frequency with the respectiveorthogonal or statistically orthogonal chaotic spreading code CSC₁,CSC₂. An exemplary embodiment of the receiver 106 will be describedbelow in relation to FIG. 8.

Generation of Protected Data Communication Signal 128 Shown in FIG. 1A

The generation of protected data communication signal 128 shall now bedescribed in relation to FIGS. 2A-5. To simplify the description of theformation of the protected data signal, the PAM signal with protecteddata 120 will be described in terms of only the magnitude of theamplitude modulated signal which can be viewed as a unipolar pulseamplitude modulated (PAM) signal. In the case of the punctured QAMconstellation described above, the phase modulation is ignored as it isidentical to the phase modulation of a QAM signal which is well known tothose having ordinary skill in the art. It should be noted that some ofthe amplitudes (amplitudes and magnitudes are equivalent for positiveunipolar signals) shown in FIG. 2B are associated with protected datawhile the phase angles are associated with global data in the context ofthe current invention.

Note that the PAM portion of signal 120 has statistical artifacts due tothe periodicity of the modulation that can be used so as to compromisethe security of the protected data. As such, the data communicationsignals 128, 134 can be generated using a method for removingstatistical artifacts from the PAM signal 120. In effect, the securityof all data can be increased as compared to conventional multiple accesscommunications systems.

Referring now to FIG. 2A, there is provided a conceptual diagram of amethod for removing statistical artifacts from the PAM signal 120 thatassumes combination of the PAM signal 120 with a separable complementthereof. The separable complement is referred to as complementary signal122. Notably, signals 120 and 122 as shown in FIG. 2A are not separabledirectly based on amplitudes. However, signals 120 and 122 will be shownin subsequent paragraphs to be made separable by virtue of orthogonalspreading sequences.

As shown in FIG. 2A, PAM signal 120 has cyclostationary signalproperties resulting from its periodically changing amplitude andtherefore its periodically changing transmitted power. In effect, anoutside observer can obtain information about the PAM signal 120 simplyby identifying the periodic nature of the symbol energy. Consequently,it is desirable to process the PAM signal 120 to reduce or eliminate thecyclostationary properties from the transmitted signal. This isaccomplished by means of power adjustment processing (PAP) 202. PAP 202generates the data communication signal 128 having a constant powerenvelope. The result is that the data communication signal 128 has apower or variance that does not change in statistical expectation overtime. An exemplary PAP 202 will now be described in relation to FIGS.2B-3.

Referring now to FIG. 2B, there is provided a conceptual illustration ofan exemplary PAP 202 that is useful for understanding the presentinvention. As shown in FIG. 2B, PAP 202 generally involves combining thesquare root of the amplitudes AV (expressed in volts) of the PAM signal120 for each symbol period SP with the square root of the amplitudes CV(expressed in volts) of the complementary PAM signal 122 such that thesum of the resulting average power O remain constants. For convenience,the amplitude AV of the PAM signal 120 for each symbol period SP shallbe referred to herein as AV(SP_(n)), where n is the index number of aparticular symbol period SP. Thus, the amplitude AV of the PAM signal120 for the first symbol period SP₁ is AV(SP₁). Similarly, the amplitudeAV of the PAM signal 120 for the second index period SP₂ is AV(SP₂), andso on. The amplitude CV of the complementary PAM signal 122 for eachsymbol period SP shall be referred to herein as CV(SP_(n)), where n isthe index number of a particular symbol period SP. The amplitude CV ofthe complementary PAM signal 122 for the first symbol period SP₁ isCV(SP₁). Likewise, the amplitude CV of the complementary PAM signal 122for the second index period SP₂ is CV(SP₂), and so on.

Such combining operations can be defined by the following mathematicalequations (1)-(3) that represent the per symbol power of the signal byadding the symbol power and complementary symbol power. For simplicity,let the symbol voltages drive a one (1) ohm load. Since power equalsvoltage squared divided by resistance, setting resistance to one (1) ohmsimplifies the power calculations toO(SP_(n))=|A(SP_(n))|²+|C(SP_(n))|².O(SP ₁)=|AV(SP ₁)|²/1Ω+|CV(SP ₁)|²/1Ω  (1)O(SP ₂)=|AV(SP ₂)|²/1Ω+|CV(SP ₂)|²/1Ω  (2)O(SP ₃)=|AV(SP ₃)|²/1Ω+|CV(SP ₃)|²/1Ω  (3)where O(SP₁) is a power of the protected data communication signal 128for a first output symbol period. O(SP₂) is a power of the protecteddata communication signal 128 for a second output symbol period. O(SP₃)is a power of the protected data communication signal 128 for a thirdoutput symbol period. AV(SP₁) is an amplitude of the PAM signal 120 fora first symbol period. AV(SP₂) is an amplitude of the PAM signal 120 fora second symbol period. AV(SP₃) is an amplitude of the PAM signal 120for a third symbol period. CV(SP₁) is an amplitude of the complementaryPAM signal 122 for a first symbol period. CV(SP₂) is an amplitude of thecomplementary PAM signal 122 for a second symbol period. CV(SP₃) is anamplitude of the complementary PAM signal 122 for a third symbol period.

Referring again to FIG. 2B, PAP 202 produces a constant power envelopesignal as is desirable for the protected data communication signal 128.However, PAP 202 does not produce a separable signal combination. Thephrase “separable signal”, as used herein, refers to a signal havingseparable signal components, wherein a first signal component isorthogonal or statistically orthogonal to all other signal components.One can appreciate that this non-separable signal combination isundesirable in a communications system application since there is nodistinction, and therefore no useable information, between the directcombination of PAM signals 120, 122. As such, PAP 202 needs improvementso that the combination of the PAM signal 120 and the complementary PAMsignal 122 is a separable signal combination. Such an improved PAP 202will now be described in relation to FIGS. 2C and 3.

Referring now to FIG. 2C, the improved PAP 202 generally involvesperforming combination (or multiplication) operations 226, 228 utilizingorthogonal or statistically orthogonal signals (e.g., Gaussian randomnumber sequences 280, 282) and an addition operation 230. It should benoted that the orthogonal or statistically orthogonal signal 280represents the first chaotic spreading code CSC₁ of FIG. 1A. Similarly,the orthogonal or statistically orthogonal signal 282 represents thesecond chaotic spreading code CSC₂ of FIG. 1A. As used herein, the termstatistically orthogonal signal may be applied to signals or discretesequences, to indicate that the stationary statistical expectation ofthe inner product of two or more signals is zero (0). One typicalexample of orthogonal signals, in practical use, is the sine and cosinefunctions. In communications systems employing chaotic spreadingsequences, the statistically orthogonal signals can be expressed asindependent quadrature Gaussian random number sequences. For example, afirst Gaussian random number sequence 280 can be generated using arandom number generation operator 232. The first Gaussian random numbersequence 280 can be defined as the sequence of random numbers FSRN₁,FSRN₂, FSRN₃, . . . , FSRN_(M). A second Gaussian random number sequence282 can be generated using a random number generation operator 234. Thesecond Gaussian random number sequence 282 can be defined as the secondsequence of random numbers SSRN₁, SSRN₂, SSRN₃, . . . , SSRN_(M). Insuch a scenario, the Gaussian random number sequences 280, 282 can begenerated utilizing two (2) statistically independent Gaussian randomnumber generators, Gaussian pseudo-random number generators, or Gaussianchaotic number generators.

If the Gaussian random number sequences 280, 282 are generated usingGaussian-distributed chaotic number generators, then the random numbersequences 280, 282 are chaotic number sequences. It should be understoodthat a mathematically chaotic signal based on a chaotic number sequencecan be made to present itself as a noise signal having a Gaussiandistribution. The Gaussian distribution is well known to those havingordinary skill in the art, and therefore will not be described herein.However, it should be appreciated that the power of the chaotic signalis measured as the variance of the Gaussian noise distribution. It isdesirable to have the variance of the sum of the products of thecombination (or multiplication) operations 226, 228 to equal a constantvariance (or power) in statistical expectation. This constant varianceneed not be obtained from two (2) equal variance signals. Although, bothrandom number generators 232, 234 can be selected to have standardnormal (Gaussian) distributions with zero (0) mean and unit variance.

The combination (or multiplication) operations 226, 228 can be definedby mathematical equations (4) and (5) assuming a normalized resistanceof one (1) ohm.FPS=PAMS·FOS=[sqrt[AV(SP ₁)]·FSRN ₁ ], [sqrt[AV(SP ₁)]·FSRN ₂ ],[sqrt[AV(SP ₁)]·FSRN ₃ ], . . . , [sqrt[AV(SP ₁)]·FSRN _(M/N) ], [AV(SP₂)]·FSRN _(M/N+1) ],[AV(SP ₂)]·FSRN _(M/N+2) ], . . . , [AV(SP ₂)]FSRN_(2M/N) ], [AV(SP ₃)]·FSRN _(2M/N+1)],  (4)SPS=CS·SOS=[sqrt[CV(SP ₁)]·SSRN ₁ ],[sqrt[CV(SP ₁)]·SSRN ₂ ],[sqrt[CV(SP₁)]·SSRN ₃ ], . . . , [sqrt[CV(SP ₁)]·SSRN _(M/N]) , [sqrt[CV(SP₂)]·SSRN_(M/N+1) ],[sqrt[CV(SP ₂)]·SSRN _(M/N+2) ], . . . , [sqrt[CV(SP₂)]·SSRN _(2M/N) ],[sqrt[CV(SP ₃)]·SSRN _(2M/N+1)],  (5)where FPS is a first product signal 124 resulting from themultiplication of the square root of an amplitude of the PAM signal 120and a first orthogonal or statistically orthogonal signal 280. SPS is asecond product signal 126 resulting from the multiplication of thesquare root of an amplitude of the complementary PAM signal 122 and asecond orthogonal or statistically orthogonal signal 282. PAMS is themagnitude square root of PAM signal 120. CS is the magnitude square rootof complementary PAM signal 122. FOS is the first orthogonal orstatistically orthogonal signal 280. SOS is the second orthogonal orstatistically orthogonal signal 282.

The addition operation 230 can be defined by the following mathematicalequation (6).DCS=FPS+SPS=[(sqrt[AV(SP ₁)]·FSRN ₁)+(sqrt[CV(SP ₁)]·SSRN ₁)], . . . ,[(sqrt[AV(SP ₂)]·FSRN _(L+1))+(sqrt[CV(SP ₂)]·SSRN _(L+1))],  (6)where DCS is the protected data communication signal 128 resulting fromthe combination of the FPS 124 resulting from a first multiplicationoperation defined above in relation to mathematical equation (4) withthe SPS 126 resulting from a first multiplication operation definedabove in relation to mathematical equation (5).

Notably, the protected data communication signal 128 is a separablesignal if FOS and SOS are known separately. Stated differently, theprotected data communication signal 128 is comprised of separablecomponents, namely FPS 124 and SPS 126. The signal components FPS 124and SPS 126 can be separated utilizing correlation operations as shownin FIG. 3. Such correlation operations are well known to those havingordinary skill in the art, and therefore will not be described herein.However, it should be understood that any suitable correlation operationcan be used without limitation, where the received signal is correlatedagainst the locally generated, time synchronized, replicas of thespreading sequences used at the transmitter, CSC₁′ and CSC₂′, asdescribed previously.

If only the sum (FOS+SOS) is known (as is the case at a partialpermission receiver 108), then the global data can be retrieved usingcorrelation techniques while simultaneously separable protected dataspread respectively by FOS and SOS cannot be retrieved.

Referring now to FIG. 4, there is a method 400 for generating a chaoticamplitude modulated signal absent of cyclostationary features and havingseparable signal components. As shown in FIG. 4, the method 400 beginsat step 402 and continues with step 404. In step 404, a PAM signal 120for the protected data signal is generated. The PAM signal 120 has apulse amplitude modulated component. As stated above, the PAM signal 120has a periodically changing amplitude (or magnitude). The PAM signal 120can be generated in accordance with any known discrete time amplitudemodulation scheme.

Thereafter, the method continues with step 406. In step 406, a firstpart of the protected data communication signal 128 (FP₁₂₈) is generatedby replacing the amplitude of the PAM signal 120 by the square root ofthe magnitude values |AV(SP₁)|, |AV(SP₂)|, |AV(SP₃)|, . . . ,|AV(SP_(N))| of the PAM signal 120. Notably, dividing a nonzero unsignednumber by the square root of its magnitude is equivalent to taking thesquare root of the magnitude of a that number.

In step 408, a complementary PAM signal 122 is generated for theprotected data communication signal 128. The complimentary PAM signal122 is the second part of the PAM data communication signal 128. Thecomplementary PAM signal 122 is a signal with the same phase (and thusthe same sign) as the PAM signal 120. The complementary PAM signal 122has a magnitude that is one minus the magnitude of the PAM signal 120.

Thereafter, the method continues with step 410. In step 410, a secondpart of the data communication signal 128 (SP₁₂₈) is generated byreplacing the amplitude of the complementary PAM signal 122 by thesquare root of the magnitude values 1−|AV(SP₁)|, 1−|AV(SP₂)|,1−|AV(SP₃)|, . . . , 1−|AV(SP_(N))| of the PAM signal 120 where|AV(SP_(n))| is assumed to be normalized to be less than one (1). Insuch a scenario, the complementary PAM signal 122 has magnitude valuesdefined by the following mathematical equations (7)-(9).|CV(SP ₁)|=sqrt(1−|AV(SP ₁)|)  (7)|CV(SP ₂)|=sqrt(1|AV(SP ₂)|)  (8)|CV(SP _(N))|=sqrt(1−|AV(SP _(N))|)  (9)where |CV(SP₁)| is a first magnitude value of the complementary PAMsignal 122. |CV(SP₂)| is a second magnitude value of the complementaryPAM signal 122. |CV(SP_(N))| is an N^(th) magnitude value of thecomplementary PAM signal 122. Embodiments of the present invention arenot limited in this regard. In particular, the amplitude (or magnitude)of the PAM signal 120 may be scaled or normalized to fit within theframework shown in FIG. 4.

Upon completing step 410, the method 400 continues with step 412. Instep 412, a first Gaussian random number sequence (FGRNS) and a secondGaussian random number sequence (SGRNS) are generated. FGRNS behaveslike a first statistically orthogonal signal (FOS). FGRNS is comprisedof the random number sequence FSRN₁, FSRN₂, FSRN₃, . . . , FSRN_(M). Therandom number sequence FSRN₁, FSRN₂, FSRN₃, . . . , FSRN_(M) can be atrue random number sequence, a pseudo-random number sequence, or achaotic number sequence. Similarly, SGRNS behaves like a secondstatistically orthogonal signal (SOS). SOS is orthogonal orstatistically orthogonal to the FOS. SGRNS is comprised of the randomnumber sequence SSRN₁, SSRN₂, SSRN₃, . . . , SSRN_(M). The random numbersequence SSRN₁, SSRN₂, SSRN₃, . . . , SSRN_(M) can be a true randomnumber sequence, a pseudo-random number sequence, or a chaotic numbersequence. Notably, the stationary statistical expectation of FOS and SOSis zero (0). FOS and SOS are generated at an identical rate which issubstantially greater than a symbol rate.

After generating the FGRNS and SGRNS, step 414 is performed. In step414, a first product signal (FPS) 124 is generated by multiplying symbolvalues of the PAM signal 120 by respective random number values of theFGRNS. For example, if FP₁₂₈ is comprised of a plurality of pulseamplitude modulated (PAM) symbol periods, then a first PAM symbolA_(sym)(SP₁) of a first PAM symbol period is multiplied by a firstrandom number FSRN₁ through the L^(th) random number FSRN_(M/N) of theFGRNS, i.e. A_(sym)(SP₁)·FSRN₁, A_(sym)(SP₁)·FSRN₂, . . . ,A_(sym)(SP₁)·FSRN_(M/N), where M/N=L is the system's spreading ratio.Similarly, a second PAM symbol A_(sym)(SP₂) of a second PAM symbolperiod is multiplied by a second sequence of random numbers FSRN_(M/N+1)through FSRN_(2M/N) of the FGRNS, and so on. Embodiments of the presentinvention are not limited in this regard.

In step 416, a second product signal (SPS) 126 is generated bymultiplying symbol values of the complementary PAM signal 122 byrespective random number values of the SGRNS. For example, if SP₁₂₈ iscomprised of a plurality of complementary symbol periods, then a firstPAM symbol C_(sym)(SP₁) of a first complementary symbol period ismultiplied by a first random number SSRN₁ through the L^(th) randomnumber SSRN_(M/N) of the SGRNS, i.e., C_(sym)(SP₁)·SSRN₁,C_(sym)(SP₁)·SSRN₂, . . . , C_(sym)(SP₁)·SSRN_(M/N), where M/N=L is thesystem's spreading ratio. Similarly, a second amplitude C_(sym)(SP₂) ofa second complementary symbol period is multiplied by a second randomnumber sequence SSRN_(M/N+1) through SSRN_(2M/N) of the SGRNS, and soon. Embodiments of the present invention are not limited in this regard.

After generating the FPS 124 and SPS 126, method 400 continues with step418. In step 418, the protected data communication signal 128 isgenerated by adding together each of values of the FPS 124 withrespective values of the SPS 126. Subsequently, step 420 is performedwhere method 400 ends or other processing is resumed.

Referring now to FIG. 5, there is provided a more detailed block diagramof a chaotic pulse amplitude modulation (CPAM) system 500 implementingmethod 400 (described above in relation to FIG. 4). It should be notedthat the CPAM system 500 can be implemented in the transmitter 102 ofFIG. 1A for purposes of generating the protected data communicationsignal 128. The CPAM system 500 can be implemented in the transmitter102 of FIG. 1A for purposes of generating the global data communicationsignal 134 with CV=AV for a fixed AV. In FIG. 5, A_(sym)(SP_(n)) isequal to the sign of AV(SP_(n)) times the square root of AV(SP_(n)) andC_(sym)(SP_(n)) is equal to the sign of AV(SP_(n)) times the square rootof one (1) minus the magnitude of AV(SP_(n)) as described in relation toFIG. 4. A schematic illustration of the transmitter 102 implementing aCPAM system (such as that shown in FIG. 5) is provided in FIG. 6. Thetransmitter 102 of FIG. 6 will be described below in detail.

Referring again to FIG. 5, the CPAM system 500 illustrates a generalizedapplication of the inventive concepts to discrete time amplitudemodulation. As shown in FIG. 5, the CPAM system 500 is comprised of adiscrete time baseband modulator (DTBM) 504, a discrete time basebandcomplement modulator (DTBCM) 508, Gaussian random number sequencegenerators (GRNSGs) 506, 510 and a computation device 520.

The DTBM 504 is configured to receive a serial digital data stream froman external device (e.g., a protected data generator). The DTBM 504 isalso configured to modulate a serial digital data stream in accordancewith any known discrete time amplitude modulation scheme with arestricted set of amplitudes. In embodiments of the present invention,such discrete time amplitude modulation schemes are limited to thosewith an even number of magnitudes generated by an amplitude modulationscheme whereby all magnitude pairs are symmetric about some mean valueand whereby the mean value and the complement of the mean value areequal. Embodiments of the present invention are not limited in thisregard. The DTBM 504 is also configured to communicate the PAM signal120 to the computation device 520.

The GRNSG 506 is configured to generate a first Gaussian random numbersequence (FGRNS) 280 and communicate the same to the computation device520. Similarly, the GRNSG 510 is configured to generate a secondGaussian random number sequence (SGRNS) 282 and communicate the same tothe computation device 520. Likewise, the DTBCM 508 is configured togenerate the complementary PAM signal 122 and communicate the same tothe computation device 520.

The computation device 520 is configured to process the received PAMsignal 120, complementary PAM signal 122, FGRNS 280 and SGRNS 282. Inthis regard, it should be understood that the computation device 520 iscomprised of magnitude square root operators (MSRO) 550, 552, complexmultipliers 512, 514 and a complex adder 516.

The MSRO 550 is configured to determine the square root of the magnitudeof each of the amplitudes values AV(SP₁), . . . , AV(SP_(N)) of the PAMsignal 120. Accordingly, the magnitude square root operations aredefined by the following mathematical equations (10)-(12).S ₄₅₀₋₁ =sqrt[AV(SP ₁)]  (10)S ₄₅₀₋₂ =sqrt[AV(SP ₂)]  (11)S _(450-N) =sqrt[AV(SP _(N))]  (12)where S₄₅₀₋₁ is a result of a first square root operation performed bythe MSRO 550. S₄₅₀₋₂ is a result of a second square root operationperformed by the MSRO 550. S_(450-N) is a result of an N^(th) squareroot operation performed by the MSRO 550. The MSRO 550 is furtherconfigured to communicate the results S₄₅₀₋₁, S₄₅₀₋₂, . . . , S_(450-N)of the square root operations to the complex multiplier 512.

The complex multiplier 512 is configured to perform multiplicationoperations using the results S₄₅₀₋₁, S₄₅₀₋₂, . . . , S_(450-N) of thesquare root operations and the FGRNS 280. More particularly, the complexmultiplier 512 is configured to multiply each of the results S₄₅₀₋₁,S₄₅₀₋₂, . . . , S_(450-N) by a respective random number FSRN₁, FSRN₂, .. . , FSRN_(M) of the FGRNS 280. These multiplication operations can bedefined by the following mathematical equations (13)-(15).R ₄₁₂₋₁ =S ₄₅₀₋₁ ·FSRN ₁ =sqrt|A(SP ₁)|·FSRN ₁|·angle(FSRN ₁)  (13)R _(412-N+1) =S ₄₅₀₋₂ ·FSRN _(M/N+1) =sqrt|A(SP ₂)|·|FSRN_(M/N+1)|·angle(FSRN _(M/N+1))  (14)R _(412-M) =S _(450-N) ·FSRN _(M) =sqrt|A(SP _(N))|·|FSRN_(M)|·angle(FSRN _(M))  (15)where R₄₁₂₋₁ is a result of a first multiplication operation performedby the complex multiplier 512. R₄₁₂₋₂ is a result of a secondmultiplication operation performed by the complex multiplier 512.R_(412-M) is result of an M^(th) multiplication operation performed bythe complex multiplier 512. The complex multiplier 512 is furtherconfigured to communicate a first product signal 124 including theresults R₄₁₂₋₁, R₄₁₂₋₂, . . . , R_(412-M) of the multiplicationoperations to the complex adder 516.

The DTBM 504 is configured to generate symbols with a maximum absolutemagnitude less than or equal to unity. The DTBCM 508 is configured toreceive the data stream 502 and generate a complementary PAM signal 122.Accordingly, the operations to produce the complementary PAM signal 122are defined by the mathematical equations (16)-(18).CS ₄₅₀₋₁=(1−sqrt|AV(SP ₁)|)=sqrt|CV(SP ₁)|  (16)CS ₄₅₀₋₂=(1−sqrt|AV(SP ₂)|)=sqrt|CV(SP ₂)|  (17)CS _(450-N)=(1−sqrt|AV(SP _(N))|)=sqrt|CV(SP _(N))|  (18)

The complex multiplier 514 is configured to perform multiplicationoperations using the SGRNS 282 and the results CS₄₅₀ of the square rootoperations performed by the MSRO 552. More particularly, the complexmultiplier 514 is configured to multiply each of the results CS₄₅₀₋₁,CS₄₅₀₋₂, . . . CS_(450-N) by a respective random number SSRN₁, SSRN₂, .. . , SSRN_(M) of the SGRNS 282. These multiplication operations can bedefined by the following mathematical equations (19)-(21).R ₄₁₄₋₁ =CS ₄₅₀₋₁ ·SSRN ₁  (19)R _(414-M/N) =CS ₄₅₀₋₂ ·SSRN _(M/N)  (20)R _(414-M) =CS _(450-N) ·SSRN _(M)  (21)where R₄₁₄₋₁ is a result of a first multiplication operation performedby the complex multiplier 514. R₄₁₄₋₂ is a result of a secondmultiplication operation performed by the complex multiplier 514.R_(414-M) is a result of an M^(th) multiplication operation performed bythe complex multiplier 514. The multiplier 514 is further configured tocommunicate a second product signal 126 including the results R₄₁₄₋₁,R₄₁₄₋₂, . . . , R_(414-M) of the multiplication operations to thecomplex adder 516.

The complex adder 516 is configured to generate the protected datacommunication signal 128. More particularly, the complex adder 516 isconfigured to perform addition operations using the results R₄₁₂₋₁,R₄₁₂₋₂, . . . , R_(412-M), R₄₁₄₋₁, R₄₁₄₋₂, . . . , R_(414-M) receivedfrom the complex multipliers 512, 514. These addition operations can bedefined by the following mathematical equations (22)-(24).Sum₄₁₆₋₁ =R ₄₁₂₋₁ +R ₄₁₄₋₁  (22)Sum₄₁₆₋₂ =R ₄₁₂₋₂ +R ₄₁₄₋₂  (23)Sum_(416-M) =R _(412-M) +R _(414-M)  (24)where Sum₄₁₆₋₁ is a sum of a first addition operation performed by thecomplex adder 516. Sum₄₁₆₋₂ is a sum of a second addition operationperformed by the complex adder 516. Sum_(416-M) is a sum of an M^(th)addition operation performed by the complex adder 516.

The adder 516 is further configured to communicate the protected datacommunication signal 128 to an external device (not shown). As should beunderstood, the external device (not shown) can include radio frequency(RF) hardware configured to transmit a chaotic waveform. RF hardware iswell known to those having ordinary skill in the art, and therefore willnot be described in detail herein. However, it should be understood thatthe RF hardware performs actions to process the protected datacommunication signal 128 for placing the same in a proper form fortransmission to a receiving device via a communications link. Note thatthe protected data communication signal 128 is of substantially similarformat to a independently generated sequence of Gaussian random values(not shown) since the addition of two constant variance Gaussian randomnumber sequences is again a constant variance Gaussian random numbersequence. The digital baseband chaotic modulator will be described inrelation to the transmitter architecture shown in FIG. 6, covering themodulation and transmission of any global data sequence, such as theglobal data communication signal 134, using a chaotically modulatedtransmission.

Referring again to FIG. 5, one embodiment of the present invention is aspecial case where only global data is transmitted. In this scenario,the amplitude of the protected data stream 502 is chosen to be aconstant value between zero (0) and one (1), inclusive, for all symboldurations, such that the protected data communication signal 128 isconstructed from a weighted addition of two Gaussian random numbersequences 280, 282. Embodiments of the present invention are not limitedin this regard.

As discussed above in relation to FIG. 1A, the protected datacommunication signal 128 is combined with a global data communicationsignal 134 via a digital baseband chaotic modulator to create the OCS140. The global data communication signal 134 can take the form of anydigitally modulated signal constellation, including amplitude and phasemodulation techniques. These amplitude and phase modulation techniquesare well known to those having ordinary skill in the art, and thereforewill not be described in herein. However, it should be understood thatany digital modulation format used to represent data may be used withoutlimitation. Exemplary digital modulation constellations for the globaldata communication signal 134 are shown in FIG. 1B.

Embodiments of the present invention uses only constant amplitudemodulated signal constellations for the global data communication signal134. Exemplary digital modulation constellations include those producedby BPSK, QPSK and 8PSK modulation types. Choosing a constant amplitudesignal constellation for the global data communication signal 134provides the added assurance to the communication system thattransmissions use a maximal entropy communication signal without anyadded cyclostationary signal content. An exemplary architecture tocreate this maximal entropy communication signal is described withrespect to FIG. 6. Embodiments of the present invention are not limitedin this regard.

Transmitter Architecture

Referring to FIG. 6, there is provided a block diagram of thetransmitter 102 shown in FIG. 1A. The embodiment of the transmitter 102assumes that: (1) a pulse amplitude modulation (PAM) data modulation isused in the construction of first product signal 124 and second productsignal 126, combined for the protected data communication signal 128 anda phase shift keyed (PSK) modulation is used for the global datacommunication signal 134; (2) global data is encoded in theconstant-amplitude PSK constellation; (3) protected data is encoded inthe PAM and complementary PAM signal constellations; (4) no pulseshaping is applied to data symbols; (5) modulated global data symbolsand random number generator values are generated in quadrature form; and(6) chaotic spectral spreading is performed at an intermediate frequency(IF).

The transmitter 102 is generally configured for generating quadratureamplitude-and-time-discrete baseband signals. The transmitter 102 isalso configured for spreading the quadrature amplitude-and-time-discretebaseband signals over a wide intermediate frequency band. This spreadingconsists of multiplying the quadrature amplitude-and-time-discretebaseband signals by digital chaotic sequences. The products of thesearithmetic operations are hereinafter referred to as digital chaoticsignals. In this regard, it should be understood that the transmitter102 is also configured to process the digital chaotic signals to placethe same in a proper analog form suitable for transmission over acommunications link. The transmitter 102 is further configured tocommunicate analog chaotic signals to a receiver (e.g., the receiver 106and/or 108 described above in relation to FIG. 1A) via a communicationslink.

As shown in FIG. 6, the transmitter 102 is comprised of data sources602, 660, source encoders 604, 662, symbol formatters 606, 664, anacquisition data generator 608, a transmitter controller 610, aprecision real time reference (PRTR) 612, multiplexers 614, 666, channelencoders 616, 668, complex multipliers 646, 680, 678, a complementsignal generator 682, a magnitude square root operator (MSRO) 686 andcomplex adder 684. The transmitter 102 is also comprised of chaosgenerators 618, 640 and real uniform statistics to quadrature (RUS-to-Q)Gaussian statistics mappers (RUQGs) 670, 674. The transmitter 102 isfurther comprised of an interpolator 626, a digital local oscillator(LO) 630, a real part of a complex multiplier 628, a digital-to-analogconverter (DAC) 632, an anti-image filter 634, an intermediate frequency(IF) to radio frequency (RF) conversion device 636, and an antennaelement 638.

The data source 602 is a global data source. The data source 602 isgenerally an interface configured for receiving an input signalcontaining global data from an external device (not shown). As such, thedata source 602 can be configured for receiving bits of data from theexternal data source (not shown). The data source 602 can further beconfigured for supplying bits of data to the source encoder 604 at aparticular data transfer rate.

The source encoder 604 is generally configured to encode the global datareceived from the external device (not shown) using a forward errorcorrection coding scheme. The bits of global data received at orgenerated by the source encoder 604 represent any type of informationthat may be of interest to a user. For example, the global data can beused to represent text, telemetry, audio, or video data. The sourceencoder 604 can further be configured to supply bits of global data tothe symbol formatter 606 at a particular data transfer rate.

The symbol formatter 606 is generally configured to process bits ofglobal data for forming channel encoded symbols. In embodiments of thepresent invention, the source encoded symbols are formatted intoparallel words compatible with phase shift keyed (PSK) encoding. Thesymbol formatter 606 can further be configured for communicating theformatted data to the multiplexer 614.

The symbol formatter 606 is functionally similar to a serial in/parallelout shift register where the number of parallel bits out is equal to logbase two (log₂) of the order of the channel encoder 616. According toembodiments of the present invention, the symbol formatter 606 isselected for use with a quadrature phase shift keying (QPSK) modulator.As such, symbol formatter 606 is configured for grouping two (2) bits ofglobal data together to form a QPSK symbol data word (i.e., a single twobit parallel word). Thereafter, symbol formatter 606 communicates theformatted symbol word data to the multiplexer 614. Embodiments of thepresent invention are not limited in this regard.

According to other embodiments of the present invention, symbolformatter 606 is functionally similar to a serial in/parallel out shiftregister where the number of parallel bits out is equal to log base two(log₂) of the order of the channel encoder 616. The symbol formatter 606is selected for use with a binary phase shift keying (BPSK) modulator.As such, the symbol formatter 606 is configured for mapping one bit ofdata to a BPSK symbol word. Thereafter, the symbol formatter 606communicates the BPSK symbol word data to the multiplexer 614.Embodiments of the present invention are not limited in this regard.

According to other embodiments of the present invention, the symbolformatter 606 is selected for use with an 8-ary phase shift keyingmodulator. As such, the symbol formatter 606 is configured for mappingthree (3) bits to an 8-ary PSK symbol word. Thereafter, the symbolformatter 606 communicates the 8-ary PSK symbol word data to themultiplexer 614. Embodiments of the present invention are not limited inthis regard.

According to other embodiments of the invention, the symbol formatter606 is selected for use with a sixteen quadrature amplitude modulator(16QAM). As such, the symbol formatter 606 is configured for mappingfour (4) bits to a 16QAM symbol word. Thereafter, the symbol formatter606 communicates the 16QAM symbol word data to the multiplexer 614.Embodiments of the present invention are not limited in this regard.Notably, when the symbol formatter 606 is selected for use with anon-constant amplitude data modulator, the output communication signal140 tends to have detectable cyclostationary content.

Referring again to FIG. 6, the acquisition data generator 608 isconfigured for generating a “known data preamble”. The “known datapreamble” can be a repetition of the same known symbol or a series ofknown symbols. The “known data preamble” can be used to enable initialsynchronization of chaotic sequences generated in the transmitter 102and receiver (e.g., receiver 106 and/or 108 described above in relationto FIG. 1A). The duration of the “known data preamble” is determined byan amount required by a receiver (e.g., receiver 106 and/or 108described above in relation to FIG. 1A) to synchronize with thetransmitter 102 under known worst case channel conditions. Theacquisition data generator 608 can be further configured forcommunicating the “known data preamble” to at least one of themultiplexers 614, 666.

Multiplexer 614 is configured to receive a binary word (that is to bemodulated by the channel encoder 616) from the symbol formatter 606. Themultiplexer 614 is also configured to receive the “known data preamble”from the acquisition data generator 608. The multiplexer 614 is coupledto the transmitter controller 610. The transmitter controller 610 isconfigured for controlling the multiplexer 614 so that the multiplexer614 routes the “known data preamble” to the channel encoder 616 at thetime of a new transmission.

According to alternative embodiments of the invention, the “known datapreamble” is stored in a modulated form. In such a scenario, thearchitecture of FIG. 6 is modified such that the multiplexer 614 existsafter the channel encoder 616. The “known data preamble” may also beinjected at known intervals to aid in periodic resynchronization ofchaotic sequences generated in the transmitter 102 and a receiver (e.g.,receiver 106 and/or 108 described above in relation to FIG. 1A). Thiswould typically be the case for an implementation meant to operate inharsh channel conditions. Embodiments of the present invention are notlimited in this regard.

Referring again to FIG. 6, the multiplexer 614 can be configured forselecting symbol data to be routed to the channel encoder 616 after apreamble period has expired. Multiplexer 614 can also be configured forcommunicating data symbols to the channel encoder 616. In this regard,it should be appreciated that a communication of the symbol data to thechannel encoder 616 is delayed by a time defined by the length of the“known data preamble.” This delay allows all of a “known data preamble”to be fully communicated to the channel encoder 616 prior tocommunication of the data symbols.

The channel encoder 616 can be configured for performing actions torepresent the “known data preamble” and the symbol data in the form of amodulated quadrature amplitude-and-time-discrete digital signal. Themodulated quadrature amplitude-and-time-discrete digital signal isdefined by digital words which represent intermediate frequency (IF)modulated symbols comprised of bits of global data having a one (1)value or a zero (0) value. Methods for representing digital symbols by aquadrature amplitude-and-time-discrete digital signal are well known topersons having ordinary skill in the art, and therefore will not bedescribed herein. However, it should be appreciated that the channelencoder 616 can employ any known method for representing digital symbolsby a quadrature amplitude-and-time-discrete digital signal.

As shown in FIG. 6, the channel encoder 616 can be selected as a digitalbaseband modulator employing quadrature phase shift keying (QPSK). Assuch, the output of the QPSK modulator includes an in-phase (“I”) dataand quadrature phase (“Q”) data. Accordingly, channel encoder 616 isconfigured for communicating I and Q data to the complex multiplier 644.

According to embodiments of the present invention, the transmitter 102is comprised of a sample rate matching device (not shown) betweenchannel encoder 616 and complex multiplier 646. The sample rate matchingdevice (not shown) can perform a sample rate increase on theamplitude-and-time-discrete digital signal so that a sample rate of theamplitude-and-time-discrete digital signal is the same as a digitalchaotic sequence communicated to the complex multiplier 646. Embodimentsof the present invention are not limited in this regard.

Complex multiplier 646 can be configured for performing a complexmultiplication in the digital domain. The complex multiplier 646 isconfigured to receive an input from the channel encoder 616. The complexmultiplier is further configured to receive an input from the complexadder 684. In the complex multiplier 646, the quadratureamplitude-and-time-discrete digital signal from the channel encoder 616is multiplied by the sum of the two sample rate matched chaoticsequences. The sum chaotic signal is generated in the complex adder 684.The complex multiplier 646 generates the output communication signal 140from the global data communication signal 134 and the protected datacommunication signal 128. The complex multiplier 646 is configured todeliver its output to an interpolator 626.

Data source 660 is a protected data source. Data source 660 is generallyan interface configured for receiving an input signal containingprotected data from an external device (not shown). As such, data source660 can be configured for receiving bits of data from the external datasource (not shown). Data source 660 can further be configured forsupplying bits of data to source encoder 662 at a particular datatransfer rate.

Source encoder 662 is generally configured to encode the protected datareceived from the external device (not shown) using a forward errorcorrection coding scheme. The bits of protected data received at orgenerated by the source encoder 662 represent any type of informationthat may be of interest to a user. For example, the protected data canbe used to represent text, telemetry, audio, or video data. Sourceencoder 662 can further be configured to supply bits of protected datato symbol formatter 664 at a particular data transfer rate.

The symbol formatter 664 is generally configured to process bits ofprotected data for forming channel encoded symbols. According toembodiments of the present invention, the source encoded symbols areformatted into parallel words compatible with pulse amplitude modulation(PAM) encoding. The symbol formatter 664 can further be configured forcommunicating the formatted data to the multiplexer 666.

Multiplexer 666 is generally configured for selecting symbol data to berouted to channel encoder 668 after a preamble period has expired.Multiplexer 666 can also be configured for communicating symbol data tochannel encoder 668. In this regard, it should be appreciated that acommunication of the symbol data to channel encoder 668 can be delayedby a time defined by the length of the “known data preamble.”

Channel encoder 668 is generally configured for performing actions torepresent the “known data preamble” and/or the symbol data in the formof a modulated amplitude-and-time-discrete digital signal. The modulatedamplitude-and-time-discrete digital signal is defined by digital wordswhich represent intermediate frequency (IF) modulated symbols comprisedof bits of protected data having a one (1) value or a zero (0) value.Methods for representing digital symbols by anamplitude-and-time-discrete digital signal are well known to personshaving ordinary skill in the art, and therefore will not be describedherein. However, it should be appreciated that channel encoder 668 canemploy any known method for representing digital symbols by anamplitude-and-time-discrete digital signal. Accordingly, channel encoder668 is configured for communicating amplitude data to the MSRO 686 andcomplement signal generator 682.

MSRO 686 is the same as or substantially similar to the MSRO 550 of FIG.5. As such, the description of magnitude square root operator 550provided above in relation to FIG. 5 is sufficient for understanding theoperations of MSRO 686. However, it should be understood that MSRO 686is configured for communicating results of square root operations tocomplex multiplier 678.

Complex multiplier 678 is generally configured for performing a complexmultiplication in the digital domain. In digital complex multiplier 678,a signal including results of square root operations performed by MSRO686 is multiplied by a chaotic spreading code CSC₁. Chaotic spreadingcode CSC₁ is a digital representation of a chaotic sequence. The chaoticsequence is generated by chaos generator 640 and real uniform toquadrature Gaussian statistics mapper (RUQG) 674. Chaos generator 640 isgenerally configured for generating chaotic sequences in accordance withthe methods described below in relation to FIGS. 9-10. Accordingly,chaos generator 640 employ a set of polynomial equations, a set ofconstants, and/or a set of relatively prime numbers as modulus for usein chaotic sequence generations. The rate at which the digital chaoticsequence is generated is an integer multiple of a data symbol rate. Thegreater the ratio between the data symbol period and the sample periodof the digital chaotic sequence the higher a spreading gain. Notably,chaos generator 640 can be configured for receiving initial conditionsfrom transmitter controller 610. The initial conditions define anarbitrary sequence starting location, i.e., the number of places (e.g.,zero, one, two, Etc.) that a chaotic sequence is to be cyclicallyshifted. The initial condition will be described below in relation tostep 1014 of FIG. 10. Chaos generator 640 can also be configured forcommunicating the chaotic sequence to RUQG 674.

RUQG 674 is generally configured for statistically transforming thechaotic spreading code (or chaotic sequence) into a transformed digitalchaotic sequence with pre-determined statistical properties. Thetransformed digital chaotic sequence can have a characteristic formincluding real or quadrature. The transformed digital chaotic sequencecan have different word widths and/or different statisticaldistributions. For example, RUQG 674 may take in two (2) uniformlydistributed real inputs from the chaos generator 640 and convert thosevia a complex-valued bivariate Gaussian transformation to a quadratureoutput having statistical characteristics of a Guassian distribution.Such conversion techniques are well understood by those having ordinaryskill in the art, and therefore will not be described in herein.However, it should be understood that such conversion techniques may usenonlinear processors, look-up tables, iterative processing (CORDICfunctions), or other similar mathematical processes. RUQG 674 is alsoconfigured for communicating transformed chaotic sequences to thecomplex multiplier 678.

According to embodiments of the present invention, RUQG 674statistically transforms the chaotic spreading code into a quadratureGaussian form of the digital chaotic sequence. This statisticaltransformation is achieved via a nonlinear processor that combineslookup tables and embedded computational logic to implement theconversion of two (2) independent uniformly distributed random variablesinto a quadrature pair of Gaussian distributed variables. One suchstructure for this conversion is as shown in the mathematical equations(25) and (26).G ₁=√{square root over (−2 log(u ₁))}·cos(2πu ₂)  (25)G ₂=√{square root over (−2 log(u ₁))}·sin(2πu ₂)  (26)where {u1, u2} are uniformly distributed independent input randomvariables and {G₁, G₂} are Gaussian distributed output random variables.Embodiments of the present invention are not limited in this regard. Theoutput of the RUGQ 674 is the first chaotic spreading code CSC₁.

Referring again to FIG. 6, complex multiplier 678 is configured forperforming complex-valued digital multiplication operations using thedigital chaotic sequence output from RUQG 674 and theamplitude-and-time-discrete digital signal output from the MSRO 686. Theresult of the complex-valued digital multiplication operations is adigital representation of a coherent chaotic sequence spread spectrummodulated IF signal (hereinafter referred to as a “first spread spectrumdigital chaotic signal”). The first spread spectrum digital chaoticsignal comprises digital protected data that has been spread over a widefrequency bandwidth in accordance with the chaotic spreading code CSC₁generated by components 640, 674. Complex multiplier 678 is alsoconfigured to communicate the first spread spectrum digital chaoticsignal to the complex adder 684.

Complement signal generator (CSG) 682 is the same as or substantiallysimilar to the compliment signal generator 508 of FIG. 5. As such, thedescription of the compliment signal generator 508 provided above inrelation to FIG. 5 is sufficient for understanding the operations of thecomplement signal generator 682 of FIG. 6. However, it should beunderstood that CSCG 682 is configured for generating a complimentarysignal and communicate the same to the complex multiplier 680.

Complex multiplier 680 is generally configured for performing a complexmultiplication in the digital domain. In complex multiplier 680, thecompliment signal from the CSG 682 is multiplied by a chaotic sequence.The chaotic sequence is generated by chaos generator 618. Chaosgenerator 618 is the same as or substantially similar to chaos generator640. As such, the description of chaos generator 640 is sufficient forunderstanding chaos generator 618. However, is should be noted thatchaos generator 618 is generally configured for generating chaoticsequences in accordance with the methods described below in relation toFIGS. 9-10. Chaos generator 618 is also configured for communicating thechaotic sequence to RUQG 670.

RUQG 670 is generally configured for statistically transforming chaoticsequences into transformed digital chaotic sequences with pre-determinedstatistical properties. The transformed digital chaotic sequences canhave characteristic forms including real or quadrature. The transformeddigital chaotic sequences can have different word widths and/ordifferent statistical distributions. For example, RUQG 670 may take intwo (2) uniformly distributed real inputs from chaos generator 618 andconvert those via a complex-valued bivariate Gaussian transformation toa quadrature output having statistical characteristics of a Guassiandistribution. Such conversion techniques are well understood by thosehaving ordinary skill in the art, and therefore will not be described inherein. However, it should be understood that such conversion techniquesmay use nonlinear processors, look-up tables, iterative processing(CORDIC functions), or other similar mathematical processes. RUQG 670 isalso configured for communicating transformed chaotic sequences to thecomplex multiplier 680.

According to embodiments of the present invention, RUQG 670statistically transforms the chaotic sequence into a quadrature Gaussianform of the digital chaotic sequence. This statistical transformation isachieved via a nonlinear processor that combines lookup tables andembedded computational logic to implement the conversion of two (2)independent uniformly distributed random variables into a quadraturepair of Gaussian distributed variables. One such structure for thisconversion is as shown in the above provided mathematical equations (25)and (26). Embodiments of the present invention are not limited in thisregard. The output of the RUGQ 670 is the second chaotic spreading codeCSC₂.

Referring again to FIG. 6, complex multiplier 680 is configured forperforming complex-valued digital multiplication operations using thedigital chaotic sequence output from RUQG 670 and the complimentary PAMsignal 122 output from CSG 682. The result of the complex-valued digitalmultiplication operations is a digital representation of a coherentchaotic sequence spread spectrum modulated IF signal (hereinafterreferred to as a “second spread spectrum digital chaotic signal”). Thesecond spread spectrum digital chaotic signal comprises digitalprotected data that has been spread over a wide frequency bandwidth inaccordance with the chaotic sequence generated by chaos generator 618.Complex multiplier 680 is also configured to communicate the secondspread spectrum digital chaotic signal to complex adder 684.

Complex adder 684 is configured for generating the protected datacommunication signal 128 shown in FIG. 1A. In this regard, it should beunderstood that complex adder 684 is the same as or substantiallysimilar to the complex adder 516 of FIG. 5. As such, the description ofcomplex adder 516 provided above in relation to FIG. 5 is sufficient forunderstanding the operations of complex adder 684. However, it should beunderstood that complex adder 684 is configured for communicating theprotected data communication signal 128 to the complex multiplier 646.Complex multiplier 646 is configured for generating the outputcommunication signal 140 of FIG. 1A by performing complex multiplicationoperations using the amplitude-and-time-discrete digital signal (orglobal data communication signal 134 of FIG. 1A) from the channelencoder 616 and the protected data communication signal 128 from complexadder 684. Complex multiplier 646 is also configured for communicatingthe output communication signal 140 to interpolator 626.

Interpolator 626, real part of complex multiplier 628, and quadraturedigital local oscillator 630 form at least one intermediate frequency(IF) translator. IF translators are well known to persons havingordinary skill in the art, and therefore will not be described herein.However, it should be understood that components 626, 628, 630 can becollectively configured for frequency modulating a signal received fromcomplex multiplier 646 to a sampled spread spectrum digital chaoticsignal. The IF translator (i.e., component 628) is configured forcommunicating the sampled spread spectrum digital chaotic signal to theDAC 632, wherein the sampled spread spectrum digital chaotic signal hasan increased sampling rate and a non-zero intermediate frequency. DAC632 can be configured for converting the sampled spread spectrum digitalchaotic signal to an analog signal. DAC 632 can also be configured forcommunicating the analog signal to anti-image filter 634.

Anti-image filter 634 is configured for removing spectral images fromthe analog signal to form a smooth time domain signal. Anti-image filter634 is also configured for communicating a smooth time domain signal tothe RF conversion device 636. RF conversion device 636 can be a widebandwidth analog IF-to-RF up converter. RF conversion device 636 isconfigured for forming an RF signal by centering a smooth time domainsignal at an RF for transmission. RF conversion device 636 is alsoconfigured for communicating RF signals to a power amplifier (notshown). The power amplifier (not shown) is configured for amplifying areceived RF signal. The power amplifier (not shown) is also configuredfor communicating amplified RF signals to an antenna element 638 forcommunication to a receiver (e.g., receiver 106 and/or 108 describedabove in relation to FIG. 1A).

It should be understood that the digital generation of the digitalchaotic sequences at transmitter 102 and receivers (e.g., receiver 106and/or 108 described above in relation to FIG. 1A) is kept closelycoordinated under the control of a precision real time reference 612clock. If the precision of the clock 612 is relatively high, then thesynchronization of the chaos generators 618, 640 of transmitter 102 andthe chaos generators (described below in relation to FIG. 7A, FIG. 7B,FIG. 8A and FIG. 8B) of the receivers 106, 108 is relatively close.Precision real time reference 612 allows the states of the chaosgenerators to be easily controlled with precision.

Receiver Architectures

Referring now to FIG. 7A and FIG. 7B, there is provided a more detailedblock diagram of receiver 106 of FIG. 1A. Receiver 106 is generallyconfigured for receiving transmitted analog chaotic signals from thetransmitter (e.g., transmitter 102 described above in relation to FIG.1A and FIG. 6). Receiver 106 is also generally configured for downconverting and digitizing a received analog chaotic signal. As shown inFIG. 7A, receiver 106 comprises an antenna element 702, a low noiseamplifier (LNA) 704, a zonal filter 706, an automatic gain control (AGC)amplifier 708, a radio frequency (RF) to intermediate frequency (IF)conversion device 710, an anti-alias filter 712, and ananalog-to-digital (A/D) converter 714.

Antenna element 702 is generally configured for receiving an analoginput signal communicated from a transmitter (e.g., transmitter 102described above in relation to FIG. 1A and FIG. 6) over a communicationslink (e.g., communications link 104 described above in relation to FIG.1A). Antenna element 702 can also be configured for communicating theanalog input signal to LNA 704. LNA 704 is generally configured foramplifying a received analog input signal while adding as little noiseand distortion as possible. LNA 704 can also be configured forcommunicating an amplified, analog input signal to zonal filer 706.Zonal filter 706 is configured for suppressing large interfering signalsoutside of bands of interest. Zonal filter 706 can also be configuredfor communicating filtered, analog input signals to the AGC amplifier708. AGC amplifier 708 is generally a controllable gain amplifierconfigured for adjusting a gain of an analog input signal. The AGCamplifier is configured to accept a signal from the Zonal filter 706 andthe AGC control signal 780. AGC amplifier 708 is configured forcommunicating gain adjusted, analog input signals to the RF-to-IFconversion device 710.

RF-to-IF conversion device 710 is generally configured for mixing ananalog input signal to a particular IF. RF-to-IF conversion device 710is also configured for communicating mixed analog input signals toanti-alias filter 712. Anti-alias filter 712 is configured forrestricting a bandwidth of a mixed analog input signal. Anti-aliasfilter 712 is also configured for communicating filtered, analog inputsignals to A/D converter 714. A/D converter 714 is configured forconverting received analog input signals to digital signals. A/Dconverter 714 is also configured for communicating digital input signalsto multipliers 716, 718.

Receiver 106 further includes a quadrature digital local oscillator(QDLO) 722, frequency control word 782, phase control word 784, andlowpass filters 790, 792.

Receiver 106 can also be configured for obtaining protected data encodedin the first product signal 124 from the transmitted analog chaoticsignal by correlating it with a replica of the chaotic sequencesgenerated by chaos generator 640 of the transmitter (e.g., transmitter102 described above in relation to FIG. 1A and FIG. 6). Similarly,receiver 106 can be configured for obtaining protected data encoded inthe second product signal 126 from the transmitted analog chaotic signalby correlating it with a replica of the chaotic sequences generated bychaos generator 618 of the transmitter (e.g., transmitter 102 describedabove in relation to FIG. 1A and FIG. 6). Likewise, receiver 106 can beconfigured for obtaining global data from the transmitted analog chaoticsignal by correlating it with a de-spreading code defined by the sum ofthe chaotic sequences generated by chaos generators 640, 618 of thetransmitter (e.g., transmitter 102 described above in relation to FIG.1A and FIG. 6). The global data can be converted into text, sound,pictures, navigational-position information, and/or any other type ofuseful payload information that can be communicated. Likewise, theprotected data can be converted into text, sound, pictures,navigational-position information, and/or any other type of usefulpayload information that can be communicated.

Notably, receiver 106 of FIG. 7A and FIG. 7B is designed to eliminatethe drawbacks of conventional analog based coherent communicationssystems. In this regard, it should be understood that analog chaoscircuits of conventional analog based coherent communications systemsare synchronized by periodically exchanging state information. Theexchange of state information requires a substantial amount ofadditional bandwidth. In contrast, receiver 106 is configured tosynchronize strings of discrete time chaotic samples (i.e., chaoticsequences) without using a constant or periodic transfer of state updateinformation. This synchronization feature of receiver 106 will becomemore apparent as the discussion progresses.

As shown in FIG. 7B, receiver 106 further comprises a channel encodedacquisition data generator (CEADG) 750, a symbol timing recovery circuit726, a receiver controller 738, and a precision real time referenceclock 736. Receiver 106 also includes one or more correlators 728, 770,772, acquisition correlator, 754, protected data decision device 774,global data decision device 766, protected data source decoder 776,global data source data decoder 768, and complex multiplier 752.Receiver 106 further comprises one or more chaos generators 740, 760,real uniform statistic to quadrature Gaussian statistic mappers (RUQGs)742, 762, re-sampling filters 744, 764, complex adder 746, and loopcontrol circuit 720. It should be noted that the functions of the RUQGs742, 762, can be performed by the chaos generators 740, 760. In such ascenario, receiver 106 is absent of the RUQG(s) 742, 762.

QDLO 722 shown in FIG. 7A is generally configured for generating acomplex quadrature amplitude-and-time-discrete digital sinusoid at agiven frequency. The digital sinusoid can be generated using a binaryphase control word 784 and a binary frequency control word 782 receivedfrom the loop control circuit 720. QDLO 722 is also configured forcommunicating digital words representing in-phase components of thedigital sinusoid to the complex multiplier 716. QDLO 722 is furtherconfigured for communicating digital words representing quadrature-phasecomponents of the digital sinusoid to the complex multiplier 718.

Complex multiplier 716 is configured for receiving digital words fromthe A/D converter 714 and digital words from the in-phase component ofthe QDLO 722. Complex multiplier 716 is also configured for generatingdigital output words by multiplying digital words from A/D converter 714by digital words from the QDLO 722. Complex multiplier 716 is furtherconfigured for communicating real data represented as digital outputwords to lowpass filter 790.

Complex multiplier 718 is configured for receiving digital words fromA/D converter 714 and digital words from the quadrature-phase componentof the QDLO 722. Complex multiplier 718 is also configured forgenerating digital output words by multiplying the digital words fromA/D converter 714 by the digital words from QDLO 722. Complex multiplier718 is further configured for communicating imaginary data representedas digital output words to lowpass filter 792.

Lowpass filter 790 is configured to receive the real digital data frommultiplier 716 and lowpass filter the real data to generate the in-phasedigital data component of the quadrature baseband form of the receivedsignal. Lowpass filter 790 is further configured to communicate thein-phase digital output words to acquisition correlator 754 andcorrelators 770, 772, 728. Lowpass filter 792 is configured to receivethe imaginary digital data from multiplier 718 and lowpass filter theimaginary data to generate the quadrature-phase digital data componentof the quadrature baseband form of the received signal. Lowpass filter792 is further configured to communicate the in-phase digital outputwords to acquisition correlator 754 and correlators 770, 772, 728.

It should be noted that the functional blocks hereinafter described inFIG. 7B represent three channel devices in the sense that the same orsimilar functions are being performed concurrently for purposes ofextracting global data and protected data. In this regard, it will berecalled that protected data communication signal 128 includes protecteddata signal 120 and complimentary protected data signal 122.

Complex correlators 728, 770, 772 are configured for performing complexcorrelations in the digital domain. Each of the complex correlators cangenerally involve multiplying digital words received from multipliers716, 718 (filtered by lowpass filters 790, 792) by digital wordsrepresenting a chaotic sequence and computing a complex sum of productswith staggered temporal offsets. The chaotic sequences are generated bychaos generators 740, 760, RUQGs 742, 762, or the sum of the twosequences. A first one of the chaotic sequences CSC₁′ is a replica of achaotic sequence CSC, generated by chaos generator 640 and RUQG 674 ofthe transmitter (e.g., transmitter 102 described above in relation toFIG. 1A and FIG. 6). The first chaotic sequence CSC₁′ is synchronized intime and frequency with the chaotic sequence CSC₁ generated by chaosgenerator 640 and RUQG 674 of the transmitter (e.g., transmitter 102described above in relation to FIG. 1A and FIG. 6). A second one of thechaotic sequences CSC₂′ is a replica of a chaotic sequence CSC₂generated by chaos generator 618 and RUQG 670 of the transmitter (e.g.,transmitter 102 described above in relation to FIG. 1A and FIG. 6). Thesecond chaotic sequence CSC₂′ is synchronized in time and frequency withthe chaotic sequence CSC₂ generated by chaos generator 618 and RUQG 670of the transmitter (e.g., transmitter 102 described above in relation toFIG. 1A and FIG. 6). A third one of the chaotic sequences is a globalde-spreading code. The global de-spreading code is generated byadditively combining the first and second chaotic sequences(CSC₁′+CSC₂′).

The first and second chaotic sequences CSC₁′, CSC₂′ are generallygenerated in accordance with the methods described below in relation toFIGS. 9-10. Accordingly, chaos generators 740, 760 employ sets ofpolynomial equations, sets of constants, and/or sets of relatively primenumbers as modulus for use in chaotic sequence generations. Chaosgenerators 740, 760 can be configured for receiving initial conditionsfrom receiver controller 738. The initial conditions define arbitrarysequence starting locations, i.e., the number of places (e.g., zero,one, two, etc.) that chaotic sequences are to be cyclically shifted. Theinitial conditions will be described below in relation to step 1014 ofFIG. 10.

Chaos generator 740 is configured for communicating its chaotic sequenceto the RUQG 742. Chaos generator 760 is configured for communicating itschaotic sequence to the RUQG 762. In this regard, it should beappreciated that chaos generators 740, 760 are coupled to receivercontroller 738. Receiver controller 738 is configured to control chaosgenerators 740, 760 so that chaos generators 740, 760 generate chaoticsequences with the correct initial state when receiver 106 is in anacquisition mode and a tracking mode.

RUQGs 742, 762 are configured for statistically transforming digitalchaotic sequences into transformed digital chaotic sequences. Each ofthe transformed digital chaotic sequences has a characteristic form. Thecharacteristic form can include, but is not limited to, real, complex,quadrature, and combinations thereof. Each of the transformed digitalchaotic sequences can have different word widths and/or differentstatistical distributions. RUQGs 742, 762 are also configured forcommunicating transformed chaotic sequences to re-sampling filters 744,764.

According to the embodiment of the invention, RUQGs 742, 762 areconfigured for statistically transforming digital chaotic sequences intoquadrature Gaussian forms of the digital chaotic sequences. RUQGs 742,762 are also configured for communicating quadrature Gaussian form ofthe digital chaotic sequences to the re-sampling filters 744, 764. Moreparticularly, RUQGs 742, 762 communicate in-phase (“I”) data andquadrature phase (“Q”) data to the re-sampling filters 744, 764.Embodiments of the present invention are not limited in this regard.

Referring again to FIG. 7B, re-sampling filters 744, 764 are configuredfor forwarding transformed chaotic sequences CSC₁′, CSC₂′ to the complexcorrelators 770, 772, and complex adder 746. Re-sampling filters 744,764 are also configured for making chaos sample rates compatible with areceived signal sample rate when receiver 106 is in acquisition mode.Re-sampling filters 744, 764 are further configured to compensate fortransmit and receive clock offsets with less than a certain level ofdistortion when receiver 106 is in a steady state demodulation mode. Inthis regard, it should be appreciated that re-sampling filters 744, 764are configured for converting the sampling rates of in-phase (“I”) andquadrature-phase (“Q”) data sequences from first sampling rates tosecond sampling rates without changing the spectrum of the datacontained therein. Re-sampling filters 744, 764 are configured tocommunicate in-phase (“I”) and quadrature-phase (“Q”) data sequences tocomplex correlators 770, 772 and complex adder 746.

It should be noted that if a sampled form of a chaotic sequence isthought of as discrete samples of a continuous band limited chaos thenre-sampling filters 744, 764 are effectively tracking the discrete timesamples, computing continuous representations of the chaotic sequences,and re-sampling the chaotic sequences at the discrete time pointsrequired to match the discrete time points sampled by the A/D converter714. In effect, input values and output values of each re-samplingfilter 744, 764 are not exactly the same because the values are samplesof the same waveform taken at slightly offset times. However, the valuesare samples of the same waveform so the values have the same powerspectral density.

Referring again to FIG. 7B, complex adder 746 is configured to receiveCSC₁′ from resampling filter 744 and to receive CSC₂′ from resamplingfilter 764 and to compute global data chaotic sequence CSC₁′+CSC₂′.Complex adder 746 is also configured to output the global chaoticsequence to global correlator 728. In the embodiment shown in FIG. 7B,initial time, phase and frequency offset acquisition is performed usingthe global chaotic sequence CSC₁′+CSC₂′. Complex adder 746 is alsoconfigured to output the global chaotic sequence to complex multiplier752. In other embodiments of the present invention, initial time, phaseand frequency offset acquisition may be performed using the globalchaotic sequences CSC₁′ or CSC₂′.

Referring again to FIG. 7B, CEADG 750 is configured for generatingmodulated acquisition sequences. CEADG 750 is also configured forcommunicating modulated acquisition sequences to the complex multiplier752. Complex multiplier 752 is configured for performing complexmultiplications in the digital domain to yield references for thedigital input signal. Each of the complex multiplications can involvemultiplying a modulated acquisition sequence received from the CEADG 750by a digital representation of a global chaotic sequence. Complexmultiplier 752 is also configured for communicating reference signals tothe acquisition correlator.

Correlators 770, 772, 728 are configured to correlate locally generatedchaotic signals with the received chaotic spread signals to recover theprotected and local data. When properly aligned with symbol timing,correlator 770 recovers protected data by correlating the receivedspread signal with the chaotic sequence CSC₁′. Correlator 772 recoverscomplement protected data by correlating the received spread signal withthe chaotic sequence CSC₂′. Correlator 728 is configured for recoveringglobal data by correlating the received spread signal with the globalchaotic sequence CSC₁′+CSC₂′. In this regard, it should be understoodthat the sense of the real and imaginary components of the correlationsis directly related to the values of the real and imaginary componentsof the symbols of a digital input signal. It should also be understoodthat the magnitudes relative to a reference magnitude of the real andimaginary components of the correlation can be directly related to themagnitude values of the real and imaginary components of the amplitudemodulated symbols of a digital input signal. The reference value isdependent on the processing gain of the correlator, the gain controlvalue, and the overall gain of the receiver signal processing chain.Methods for calculating a reference magnitude are known to those havingordinary skill in the art and shall not be discussed in detail herein.Thus, the data recovery correlators include both phase and magnitudecomponents of symbol soft decisions. The phrase “soft decisions”, asused herein, refers to soft-values (which are represented bysoft-decision bits) that comprise information about the bits containedin a sequence. Soft-values are values that represent the probabilitythat a particular symbol is an allowable symbol. For example, asoft-value for a particular binary symbol can indicate that aprobability of a bit being a one (1) is p(1)=0.3. Conversely, the samebit can have a probability of being a zero (0) which is p(0)=0.7.

Similarly, at least one of the correlators is configured to facilitatesymbol timing tracking. Correlator 728 is configured for correlating achaotic sequence CSC₁′+CSC₂′ with a digital input signal on the assumedsymbol boundaries, advanced symbol boundaries, and retarded symbolboundaries. In this regard, it should be understood that, the sense andmagnitude of the real and imaginary components of the correlation isdirectly related to the time offsets of the real and imaginarycomponents of the symbols relative to actual boundaries. This symboltracking technique is well known to those having ordinary skill in theart and shall not be discussed in detail herein. It should also beunderstood that this symbol time tracking method is only one of a numberof methods known to those skilled in the art and does not limit thescope of the invention in any way. The symbol time tracking correlatoris also configured to communicate advanced, on time, and retardedcorrelation information to the symbol timing recovery block 726.

Each of the correlators 770, 772, are also configured for communicatingsoft decisions to a protected data hard decision device 774 for finalsymbol decision making. The protected data hard decision device 774 isconfigured for communicating symbol decisions to a protected data sourcedecoder 776. The protected data source decoder 776 is configured forconverting symbols to a binary form and decoding any FEC applied at atransmitter (e.g., transmitter 102 described above in relation to FIG.1A and FIG. 6). The protected data source decoder 776 is also configuredfor passing decoded bit streams to one or more external devices (notshown) utilizing the decoded protected data. The correlator 728 is alsoconfigured for communicating soft decisions to a global data harddecision device 766 for final symbol decision making. The global datahard decision device 766 is configured for communicating symboldecisions to a global data source decoder 768. The global data sourcedecoder 768 is configured for converting symbols to a binary form anddecoding any FEC applied at a transmitter (e.g., transmitter 102described above in relation to FIG. 1A and FIG. 6). The global datasource decoder 768 is also configured for passing decoded bit streams toone or more external devices (not shown) utilizing the decoded globaldata.

Acquisition Mode:

The acquisition correlator 754 is generally configured for acquiringinitial timing information associated with a chaotic sequence andinitial timing associated with a data sequence. The acquisitioncorrelator 754 is further configured for acquiring initial phase andfrequency offset information between a chaotic sequence and a digitalinput signal. Methods for acquiring initial timing information are wellknown to persons having ordinary skill in the art, and therefore willnot be described herein. Similarly, methods for acquiring initialphase/frequency offset information are well known to persons havingordinary skill in the art, and therefore will not be described herein.However, it should be appreciated that any such method for acquiringinitial timing information and/or for tracking phase/frequency offsetinformation can be used without limitation.

The acquisition correlator 754 is configured for communicating magnitudeand phase information as a function of time to the loop control circuit720. Loop control circuit 720 is configured for using magnitude andphase information to calculate a deviation of an input signal magnitudefrom a nominal range and to calculate timing, phase, and frequencyoffset information. The calculated information can be used tosynchronize a chaotic sequence with a digital input signal. Loop controlcircuit 720 is also configured for communicating phase/frequency offsetinformation to the QDLO 722 and for communicating gain deviationcompensation information to the AGC amplifier 708. Loop control circuit720 is further configured for communicating retiming control signals tore-sampling filters 744, 764 and chaos generators 740, 760.

Precision real time reference 736 is the same as or substantiallysimilar to the precision real time reference 612 of FIG. 6. Thedescription provided above in relation to the precision real timereference 612 is sufficient for understanding the precision real timereference 736 of FIG. 7B.

The operation of receiver 106 will now be briefly described with regardto an acquisition mode and a steady state demodulation mode. Inacquisition mode, re-sampling filters 744, 764 perform a rational ratechange and forwards a transformed chaotic sequences to a complex adder746. The complex adder forms the global chaotic sequence CSC₁′+CSC₂′ andoutputs it to digital complex multiplier 752. CEADG 750 generates amodulated acquisition sequence and forwards the same to a particulardigital complex multiplier 752. The complex multiplier 752 performs acomplex multiplication in the digital domain. In the complex multiplier752, a modulated acquisition sequence from the CEADG 750 is multipliedby a digital representation of a chaotic sequence to yield a referencefor a digital input signal that was generated at a transmitter (e.g.,transmitter 102 described above in relation to FIG. 1A and FIG. 6) tofacilitate initial acquisition. The chaotic sequence is generated in achaos generators 740, 760 and RUQGs 744, 764. The complex multiplier 752communicates a reference signal to the acquisition correlator 754. Inthis search mode, the acquisition correlator 754 searches across anuncertainty window to locate a received signal state so that chaosgenerators 740, 760 can be set with the time synchronized state vector.

Steady State Demodulation Mode:

In the embodiment shown in FIG. 7B, in steady state demodulation mode,correlator 728 tracks the correlation between the received modulatedsignal and the locally generated chaos close to the nominal correlationpeak to generate magnitude and phase information as a function of time.This information is passed to the loop control circuit 720. Loop controlcircuit 720 applies appropriate algorithmic processing to thisinformation to extract phase offset, frequency offset, and magnitudecompensation information. The correlator 728 also passes its outputinformation, based on correlation times terminated by symbol boundaries,to a symbol timing recovery circuit 726 and global data decision device766.

Loop control circuit 720 monitors the output of the global correlator728. When loop control circuit 720 detects fixed correlation phaseoffsets, the phase control of QDLO 722 is modified to remove the phaseoffset. When loop control circuit 720 detects phase offsets that changeas a function of time, it adjusts re-sampling filters 744, 764 which actas incommensurate re-samplers when receiver 106 is in steady statedemodulation mode or the frequency control of QDLO 722 is modified toremove frequency or timing offsets.

When the correlator's 728 output indicates that the received digitalinput signal timing has “drifted” more than plus or minus a half (½) ofa sample time relative to a locally generated chaotic sequence, loopcontrol circuit 720 (1) adjusts a correlation window in an appropriatetemporal direction by one sample time, (2) advances or retards a stateof the local chaos generators 740, 760 by one iteration state, and (3)adjusts re-sampling filters 744, 764 to compensate for the timediscontinuity. This loop control circuit 720 process keeps the chaosgenerators 618, 640 of the transmitter (e.g., transmitter 102 describedabove in relation to FIG. 1A and FIG. 6) and the chaos generators 740,760 of the receiver 106 synchronized to within half (½) of a sampletime.

If a more precise temporal synchronization is required to enhanceperformance, a re-sampling filter can be implemented as a member of theclass of polyphase fractional time delay filters. This class of filtersis well known to persons having ordinary skill in the art, and thereforewill not be described herein.

As described above, a number of chaotic samples are combined with aninformation symbol at the transmitter 102. Since the transmitter 102 andreceiver 106 timing are referenced to two (2) different precision realtime reference clock 612, 736 oscillators, symbol timing must berecovered at receiver 106 to facilitate robust demodulation. In anotherembodiment, symbol timing recovery can include (1) multiplying areceived input signal by a complex conjugate of a locally generatedchaotic sequence using a complex multiplier, (2) computing an N pointrunning average of the product where N is a number of chaotic samplesper symbol time, (3) storing the values, the maximum absolute values ofthe running averages, and the time of occurrence, and (4) statisticallycombining the values at the symbol timing recovery circuit 726 torecover symbol timing.

In this steady state demodulation mode, symbol timing recovery circuit726 communicates symbol onset timing to correlators 770, 772, 728 forcontrolling an initiation of a symbol correlation. The correlators 770,772, 728 correlates a locally generated chaotic sequence with a receiveddigital input signal during symbol duration. The sense and magnitude ofreal and imaginary components of the correlation are directly related tothe values of the real and imaginary components of symbols of a digitalinput signal. Accordingly, the correlators 770, 772, 728 generatessymbol soft decisions.

Referring now to FIGS. 8A and 8B, there is provided block diagrams of anexemplary embodiment of receiver 108 of FIG. 1A. Receiver 108 isgenerally configured for receiving transmitted analog chaotic signalsfrom a transmitter (e.g., transmitter 102 described above in relation toFIG. 1A and FIG. 6), down converting the received analog chaotic signal,and digitizing the down converted analog chaotic signal. Receiver 108 isalso generally configured for acquiring, tracking, and de-spreading atransmitted analog chaotic signal by correlating it with a de-spreadingcode. The de-spreading code is defined by the following mathematicalexpression DSC=CSC₁′+CSC₂′, where CSC₁′ and CSC₂′ are as described inrelation to FIG. 7B. Receiver 108 is further configured for processingde-spreaded analog chaotic signals to obtain global data containedtherein. The global data can be converted into text, sound, pictures,navigational-position information, and/or any other type of usefulpayload information that can be communicated.

As shown in FIG. 8A, receiver 108 is comprised of a plurality ofcomponents 802, 804, 806, 808, 810, 812, 814, 816, 818, 822, 880, 882,884, 890, 892. Components 802, 804, 806, 808, 810, 812, 814, 816, 818,822, 880, 882, 884, 890, 892 of the receiver 108 are the same as orsubstantially similar to the respective components 702, 704, 706, 708,710, 712, 714, 716, 718, 722, 780, 782, 784, 790, 792 of FIG. 7B. Assuch, the description provided above in relation to the components 702,704, 706, 708, 710, 712, 714, 716, 718, 722, 780, 782, 784, 790, 792 issufficient for understanding the components 802, 804, 806, 808, 810,812, 814, 816, 818, 822, 880, 882, 884, 890, 892. of receiver 108.

As shown in FIG. 8B, receiver 108 further comprises a channel encodedacquisition data generator (CEADG) 850, a symbol timing recovery circuit826, a receiver controller 838, and a precision real time referenceclock 836. Receiver 108 also includes global correlator 828, acquisitioncorrelator, 854, global data decision device 866, global data sourcedata decoder 868, and complex multiplier 852. Receiver 108 furthercomprises one or more chaos generators 840, 860, real uniform statisticto quadrature Gaussian statistic mappers (RUQGs) 842, 862, re-samplingfilters 844, 864, complex adder 846, and loop control circuit 820. Itshould be noted that the functions of the RUQGs 842, 862, can beperformed by the chaos generators 840, 860. In such a scenario, receiver108 is absent of the RUQG(s) 842, 862.

Components 850, 826, 838, 836, 828, 854, 866, 868, 852, 840, 860, 842,862, 844, 864, 846 of the receiver 108 are the same as or substantiallysimilar to the respective components 750, 726, 738, 736, 728, 754, 766,768, 752, 740, 760, 742, 762, 744, 764, 746 of FIG. 7B. As such, thedescription provided above in relation to the components 750, 726, 738,736, 728, 754, 766, 768, 752, 740, 760, 742, 762, 744, 764, 746 issufficient for understanding the components 850, 826, 838, 836, 828,854, 866, 868, 852, 840, 860, 842, 862, 844, 864, 846 of receiver 108.However, it should be understood that acquisition and demodulation inreceiver 108 is restricted to the global data symbols, e.g., anyinformation-bearing amplitude content can not be demodulated as CSC₁′and CSC₂′ are not independently available for exclusive despreading.

In some embodiments of the present invention, the intermediatecalculation results and other related values used to generate thedespreading sequence DSC of FIG. 8B may be intentionally masked fromaccess by the user of the partial permission receiver 104. Embodimentsof the present invention are not limited in this regard.

Chaos Generators and Digital Chaotic Sequence Generation

Referring now to FIG. 9, there is provided a conceptual diagram of achaos generator 618, 640, 740, 760, 840, 860 (described above inrelation to FIG. 6, FIG. 7B, and FIG. 8B). As shown in FIG. 9,generation of the chaotic sequence begins with N polynomial equationsf₀(x(nT)), . . . , f_(N−1)(x(nT)). The polynomial equations f₀(x(nT)), .. . , f_(N−1)(x(nT)) can be selected as the same polynomial equation oras different polynomial equations. According to an aspect of theinvention, the polynomial equations f₀(x(nT)), . . . , f_(N−1)(x(nT))are selected as irreducible polynomial equations having chaoticproperties in Galois field arithmetic. Such irreducible polynomialequations include, but are not limited to, irreducible cubic polynomialequations and irreducible quadratic polynomial equations. The phrase“irreducible polynomial equation”, as used herein, refers to apolynomial equation that cannot be expressed as a product of at leasttwo nontrivial polynomial equations over the same Galois field (GF). Forexample, the polynomial equation f(x(nT)) is irreducible if there doesnot exist two (2) non-constant polynomial equations g(x(nT)) andh(x(nT)) in x(nT) with rational coefficients such thatf(x(nT))=g(x(nT))·h(x(nT)).

Each of the polynomial equations f₀(x(nT)), . . . , f_(N−1)(x(nT)) canbe solved independently to obtain a respective solution. Each solutioncan be expressed as a residue number system (RNS) residue value usingRNS arithmetic operations, i.e., modulo operations. Modulo operationsare well known to persons having ordinary skill in the art, andtherefore will not be described herein. However, it should beappreciated that an RNS residue representation for some weighted value“a” can be defined by mathematical equation (27).R={a modulo m ₀,a modulo m ₁, . . . , a modulo m _(N−1)}  (27)where R is an RNS residue N-tuple value representing a weighted value“a” and m₀, m₁, . . . , m_(N−1) respectively are the moduli for RNSarithmetic operations applicable to each polynomial equation f₀(x(nT)),. . . , f_(N−1)(x(nT)). R(nT) can be a representation of the RNSsolution of a polynomial equation f(x(nT)) defined as R(nT){f₀(x(nT))modulo m₀, f₁(x(nT)) modulo m₁, . . . , f_(N−1)(x(nT)) modulo m_(N−1)}.

From the foregoing, it will be appreciated that the RNS employed forsolving each of the polynomial equations f₀(x(nT)), . . . ,f_(N−1)(x(nT)) respectively has a selected modulus value m₀, m₁, . . . ,m_(N−1). The modulus value chosen for each RNS moduli is preferablyselected to be relatively prime numbers p₀, p₁, . . . , p_(N−1). Thephrase “relatively prime numbers”, as used herein, refers to acollection of natural numbers having no common divisors except one (1).Consequently, each RNS arithmetic operation employed for expressing asolution as an RNS residue value uses a different prime number p₀, p₁, .. . , p_(N−1) as a moduli m₀, m₁, . . . , m_(N−1).

The RNS residue value calculated as a solution to each one of thepolynomial equations f₀(x(nT)), . . . , f_(N−1)(x(nT)) will varydepending on the choice of prime numbers p₀, p₁, . . . , p_(N−1)selected as a moduli m₀, m₁, . . . , m_(N−1). Moreover, the range ofvalues will depend on the choice of relatively prime numbers p₀, p₁, . .. , p_(N−1) selected as a moduli m₀, m₁, . . . , m_(N−1). For example,if the prime number five hundred three (503) is selected as modulus m₀,then an RNS solution for a first polynomial equation f₀(x(nT)) will havean integer value between zero (0) and five hundred two (502). Similarly,if the prime number four hundred ninety-one (491) is selected as modulusm₁, then the RNS solution for a second polynomial equation f₁(x(nT)) hasan integer value between zero (0) and four hundred ninety (490).

According to an embodiment of the invention, each of the polynomialequations f₀(x(nT)), . . . , f_(N−1)(x(nT)) is selected as anirreducible cubic polynomial equation having chaotic properties inGalois field arithmetic. Each of the polynomial equations f₀(x(nT)), . .. , f_(N−1)(x(nT)) can also be selected to be a constant or varyingfunction of time. The irreducible cubic polynomial equation is definedby a mathematical equation (28).f(x(nT))=Q(k)x ³(nT)+R(k)x ²(nT)+S(k)x(nT)+C(k,L)  (28)where:

-   x is value for a variable defining a sequence location;-   n is a sample time index value;-   k is a polynomial time index value;-   L is a constant component time index value;-   T is a fixed constant having a value representing a time interval or    increment;-   Q, R, and S are coefficients that define the polynomial equation    f(x(nT)); and-   C is a coefficient of x(nT) raised to a zero power and is therefore    a constant for each polynomial characteristic.

In embodiments of the present invention, a value of C is selected whichempirically is determined to produce an irreducible form of the statedpolynomial equation f(x(nT)) for a particular prime modulus. For a givenpolynomial with fixed values for Q, R, and S more than one value of Ccan exist, each providing a unique iterative sequence. Embodiments ofthe present invention are not limited in this regard.

According to another embodiment of the invention, the polynomialequations f₀(x(nT)), . . . , f_(N−1)(x(nT)) are identical exclusive of aconstant value C. For example, a first polynomial equation f₀(x(nT)) isselected as f₀(x(nT))=3x³(nT)+3x²(nT)+x(nT)+C₀. A second polynomialequation f₁(x(nT)) is selected as f₁(x(nT))=3x³(nT)+3x²(nT)+x(nT)+C₁. Athird polynomial equation f₂(x(nT)) is selected asf₂(x(nT))=3x³(nT)+3x²(nT)+x(nT)+C₂, and so on. Each of the constantvalues C₀, C₁, . . . , C_(N−1) is selected to produce an irreducibleform in a residue ring of the stated polynomial equationf(x(nT))=3x³(nT)+3x²(nT)+x(nT)+C. In this regard, it should beappreciated that each of the constant values C₀, C₁, . . . , C_(N−1) isassociated with a particular modulus m₀, m₁, . . . , m_(N−1) value to beused for RNS arithmetic operations when solving the polynomial equationf(x(nT)). Such constant values C₀, C₁, . . . , C_(N−1) and associatedmodulus m₀, m₁, . . . , m_(N−1) values which produce an irreducible formof the stated polynomial equation f(x(nT)) are listed in the followingTable (1).

TABLE 1 Sets of constant values Moduli values m₀, m₁, . . . , m_(N−1):C₀, C₁, . . . , C_(N−1): 3 {1, 2} 5 {1, 3} 11 {4, 9} 29 {16, 19} 47 {26,31} 59 {18, 34} 71 {10, 19, 20, 29} 83 {22, 26, 75, 79} 101 {27, 38, 85,96} 131 {26, 39, 77, 90} 137 {50, 117} 149 {17, 115, 136, 145} 167 {16,32, 116, 132} 173 {72, 139} 197 {13, 96, 127, 179} 233 {52, 77} 251 {39,100, 147, 243} 257 {110, 118} 269 {69, 80} 281 {95, 248} 293 {37, 223}311 {107, 169} 317 {15, 55} 347 {89, 219} 443 {135, 247, 294, 406} 461{240, 323} 467 {15, 244, 301, 425} 479 {233, 352} 491 {202, 234} 503 {8,271}Embodiments of the present invention are not limited in this regard.

The number of discrete magnitude states (dynamic range) that can begenerated with the system shown in FIG. 9 will depend on the quantity ofpolynomial equations N and the modulus values m₀, m₁, . . . , m_(N−1)values selected for the RNS number systems. In particular, this valuecan be calculated as the product M=m₀·m₁, m₃·m₄· . . . ·m_(N−1).

Referring again to FIG. 9, it should be appreciated that each of the RNSsolutions No. 1, . . . , No. N is expressed in a binary number systemrepresentation. As such, each of the RNS solutions No. 1, . . . , No. Nis a binary sequence of bits. Each bit of the sequence has a zero (0)value or a one (1) value. Each binary sequence has a bit length selectedin accordance with particular moduli.

According to an embodiment of the invention, each binary sequencerepresenting a residue value has a bit length (BL) defined by amathematical equation (29).BL=Ceiling[Log 2(m)]  (29)where m is selected as one of moduli m₀, m₁, . . . , m_(N−1). Ceiling[u]refers to a next highest whole integer with respect to an argument u.

In order to better understand the foregoing concepts, an example isuseful. In this example, six (6) relatively prime moduli are used tosolve six (6) irreducible polynomial equations f₀(x(nT)), . . . ,f₅(x(nT)). A prime number p₀ associated with a first modulus m₀ isselected as five hundred three (503). A prime number p₁ associated witha second modulus m₁ is selected as four hundred ninety one (491). Aprime number p₂ associated with a third modulus m₂ is selected as fourhundred seventy-nine (479). A prime number p₃ associated with a fourthmodulus m₃ is selected as four hundred sixty-seven (467). A prime numberp₄ associated with a fifth modulus m₄ is selected as two hundredfifty-seven (257). A prime number p₅ associated with a sixth modulus m₅is selected as two hundred fifty-one (251). Possible solutions forf₀(x(nT)) are in the range of zero (0) and five hundred two (502) whichcan be represented in nine (9) binary digits. Possible solutions forf₁(x(nT)) are in the range of zero (0) and four hundred ninety (490)which can be represented in nine (9) binary digits. Possible solutionsfor f₂(x(nT)) are in the range of zero (0) and four hundred seventyeight (478) which can be represented in nine (9) binary digits. Possiblesolutions for f₃(x(nT)) are in the range of zero (0) and four hundredsixty six (466) which can be represented in nine (9) binary digits.Possible solutions for f₄(x(nT)) are in the range of zero (0) and twohundred fifty six (256) which can be represented in nine (9) binarydigits. Possible solutions for f₅(x(nT)) are in the range of zero (0)and two hundred fifty (250) which can be represented in eight (8) binarydigits. Arithmetic for calculating the recursive solutions forpolynomial equations f₀(x(nT)), . . . , f₄(x(nT)) requires nine (9) bitmodulo arithmetic operations. The arithmetic for calculating therecursive solutions for polynomial equation f₅(x(nT)) requires eight (8)bit modulo arithmetic operations. In aggregate, the recursive resultsf₀(x(nT)), . . . , f₅(x(nT)) represent values in the range from zero (0)to M−1. The value of M is calculated as follows:p₀·p₁·p₂·p₃·p₄·p₅=503·491·479·467·257·251=3,563,762,191,059,523. Thebinary number system representation of each RNS solution can be computedusing Ceiling[Log 2(3,563,762,191,059,523)]=Ceiling[51.66]=52 bits.Because each polynomial is irreducible, all 3,563,762,191,059,523possible values are computed resulting in a sequence repetition time ofevery M times T seconds, i.e., a sequence repetition times an intervalof time between exact replication of a sequence of generated values.Embodiments of the present invention are not limited in this regard.

Referring again to FIG. 9, the RNS solutions No. 1, . . . , No. N aremapped to a weighted number system representation thereby forming achaotic sequence output. The phrase “weighted number system”, as usedherein, refers to a number system other than a residue number system.Such weighted number systems include, but are not limited to, an integernumber system, a binary number system, an octal number system, and ahexadecimal number system.

According to an aspect of the invention, the RNS solutions No. 1, . . ., No. N are mapped to a weighted number system representation bydetermining a series of digits in the weighted number system based onthe RNS solutions No. 1, . . . , No. N. The term “digit”, as usedherein, refers to a symbol of a combination of symbols to represent anumber. For example, a digit can be a particular bit of a binarysequence. According to another aspect of the invention, the RNSsolutions No. 1, . . . , No. N are mapped to a weighted number systemrepresentation by identifying a number in the weighted number systemthat is defined by the RNS solutions No. 1, . . . , No. N. According toyet another aspect of the invention, the RNS solutions No. 1, . . . ,No. N are mapped to a weighted number system representation byidentifying a truncated portion of a number in the weighted numbersystem that is defined by the RNS solutions No. 1, . . . , No. N. Thetruncated portion can include any serially arranged set of digits of thenumber in the weighted number system. The truncated portion can also beexclusive of a most significant digit of the number in the weightednumber system. The truncated portion can be a chaotic sequence with oneor more digits removed from its beginning and/or ending. The truncatedportion can also be a segment including a defined number of digitsextracted from a chaotic sequence. The truncated portion can further bea result of a partial mapping of the RNS solutions No. 1, . . . , No. Nto a weighted number system representation.

According to an embodiment of the invention, a mixed-radix conversionmethod is used for mapping RNS solutions No. 1, . . . , No. N to aweighted number system representation. “The mixed-radix conversionprocedure to be described here can be implemented in” [modulo modulionly and not modulo the product of moduli.] See Residue Arithmetic andIts Applications To Computer Technology, written by Nicholas S. Szabo &Richard I. Tanaka, McGraw-Hill Book Co., New York, 1967. To beconsistent with said reference, the following discussion of mixed radixconversion utilizes one (1) based variable indexing instead of zero (0)based indexing used elsewhere herein. In a mixed-radix number system, “anumber x may be expressed in a mixed-radix form:

$x = {{a_{N}{\prod\limits_{i = 1}^{N - 1}R_{i}}} + \ldots + {a_{3}R_{1}R_{2}} + {a_{2}R_{1}} + a_{1}}$where the R_(i) are the radices, the a_(i) are the mixed-radix digits,and 0≦a_(i)<R_(i). For a given set of radices, the mixed-radixrepresentation of x is denoted by (a_(n), a_(N−1), . . . , a₁) where thedigits are listed in order of decreasing significance.” See Id. “Themultipliers of the digits a_(i) are the mixed-radix weights where theweight of a_(i) is

${{{\prod\limits_{j = 1}^{i - 1}{R_{j}\mspace{14mu}{for}\mspace{14mu} i}} \neq 1.}"}\mspace{14mu}{See}\mspace{14mu}{{Id}.}$

For conversion from the RNS to a mixed-radix system, a set of moduli arechosen so that m_(i)=R_(i). A set of moduli are also chosen so that amixed-radix system and a RNS are said to be associated. “In this case,the associated systems have the same range of values, that is

$\prod\limits_{i = 1}^{N}{m_{i}.}$The mixed-radix conversion process described here may then be used toconvert from the [RNS] to the mixed-radix system.” See Id.

“If m_(i)=R_(i), then the mixed-radix expression is of the form:

$x = {{a_{N}{\prod\limits_{i = 1}^{N - 1}m_{i}}} + \ldots + {a_{3}m_{1}m_{2}} + {a_{2}m_{1}} + a_{1}}$where a_(i) are the mixed-radix coefficients. The a_(i) are determinedsequentially in the following manner, starting with a₁.” See Id.

$x = {{a_{N}{\prod\limits_{i = 1}^{N - 1}m_{i}}} + \ldots + {a_{3}m_{1}m_{2}} + {a_{2}m_{1}} + a_{1}}$is first taken modulo m₁. “Since all terms except the last are multiplesof m₁, we have <x>_(m) _(1=a) ₁. Hence, a₁ is just the first residuedigit.” See Id.

“To obtain a₂, one first forms x-a₁ in its residue code. The quantityx-a₁ is obviously divisible by m₁. Furthermore, m₁ is relatively primeto all other moduli, by definition. Hence, the division remainder zeroprocedure [Division where the dividend is known to be an integermultiple of the divisor and the divisor is known to be relatively primeto M] can be used to find the residue digits of order 2 through N of

$\frac{x - a_{1}}{m_{1}}.$Inspection of

$\left\lbrack {x = {{a_{N}{\prod\limits_{i = 1}^{N - 1}m_{i}}} + \ldots + {a_{3}m_{1}m_{2}} + {a_{2}m_{1}} + a_{1}}} \right\rbrack$shows then that x is a₂. In this way, by successive subtracting anddividing in residue notation, all of the mixed-radix digits may beobtained.” See Id.

“It is interesting to note that

${a_{1} = \left\langle x \right\rangle_{m_{1}}},{a_{2} = \left\langle \left\lfloor \frac{x}{m_{1}} \right\rfloor \right\rangle_{m_{2}}},{a_{3} = \left\langle \left\lfloor \frac{x}{m_{1}m_{2}} \right\rfloor \right\rangle_{m_{3}}}$and in general for i>1

${a_{i}{\left\langle \left\lfloor \frac{x}{m_{1}m_{2}\mspace{14mu}\ldots\mspace{14mu} m_{i - 1}} \right\rfloor \right\rangle_{m_{i}}.}}"$See Id. From the preceding description it is seen that the mixed-radixconversion process is iterative. The conversion can be modified to yielda truncated result. Embodiments of the present invention are not limitedin this regard.

According to another embodiment of the invention, a Chinese remaindertheorem (CRT) arithmetic operation is used to map the RNS solutions No.1, . . . , No. N to a weighted number system representation. The CRTarithmetic operation can be defined by a mathematical equation (30)[returning to zero (0) based indexing].

$\begin{matrix}{{Y({nT})} = \left\langle \begin{matrix}{{\left\lbrack \left\langle {\begin{pmatrix}{{3{x_{0}^{3}({nT})}} + {3x_{0}^{2}({nT})} +} \\{{x_{0}({nT})} + C_{0}}\end{pmatrix}b_{0}} \right\rangle_{p_{0}} \right\rbrack\frac{M}{p_{0}}} + \ldots +} \\{\left\lbrack \left\langle {\begin{pmatrix}{{3{x_{N - 1}^{3}({nT})}} + {3x_{N - 1}^{2}({nT})} +} \\{{x_{N - 1}({nT})} + C_{N - 1}}\end{pmatrix}b_{N - 1}} \right\rangle_{p_{N - 1}} \right\rbrack\frac{M}{p_{N - 1}}}\end{matrix} \right\rangle_{M}} & (30)\end{matrix}$where Y(nT) is the result of the CRT arithmetic operation;

-   n is a sample time index value;-   T is a fixed constant having a value representing a time interval or    increment;-   x₀, . . . , x_(N−1) are RNS solutions No. 1, . . . , No. N;-   p₀, p₁, . . . , p_(N−1) are prime numbers;-   M is a fixed constant defined by a product of the relatively prime    numbers p₀, p₁, . . . , p_(N−1); and-   b₀, b₁, . . . , b_(N−1) are fixed constants that are chosen as the    multiplicative inverses of the product of all other primes modulo    p₀, p₁, . . . , p_(N−1), respectively.    Equivalently,

$b_{j} = {\left( \frac{M}{p_{j}} \right)^{- 1}{mod}\;{p_{j}.}}$The b_(j)'s enable an isomorphic mapping between an RNS N-tuple valuerepresenting a weighted number and the weighted number. However withoutloss of chaotic properties, the mapping need only be unique andisomorphic. As such, a weighted number x can map into a tuple y. Thetuple y can map into a weighted number z. The weighted number x is notequal to z as long as all tuples map into unique values for z in a rangefrom zero (0) to M−1.

In other embodiments of the present invention, all b_(j)'s can be setequal to one or more non-zero values without loss of the chaoticproperties. For example, if b_(j)=1 for all j, Equation 30 reduces toEquation 31. The invention is not limited in this regard.

$\begin{matrix}{{Y({nT})} = \left\langle \begin{matrix}{{\left\lbrack \left\langle \begin{matrix}{{3{x_{0}^{3}({nT})}} + {3x_{0}^{2}({nT})} +} \\{{x_{0}({nT})} + C_{0}}\end{matrix} \right\rangle_{p_{0}} \right\rbrack\frac{M}{p_{0}}} + \ldots +} \\{\left\lbrack \left\langle \begin{matrix}{{3{x_{N - 1}^{3}({nT})}} + {3x_{N - 1}^{2}({nT})} +} \\{{x_{N - 1}({nT})} + C_{N - 1}}\end{matrix} \right\rangle_{p_{N - 1}} \right\rbrack\frac{M}{p_{N - 1}}}\end{matrix} \right\rangle_{M}} & (31)\end{matrix}$

Referring again to FIG. 9, the chaotic sequence output can be expressedin a binary number system representation. As such, the chaotic sequenceoutput can be represented as a binary sequence. Each bit of the binarysequence has a zero (0) value or a one (1) value. The chaotic sequenceoutput can have a maximum bit length (MBL) defined by a mathematicalequation (32).MBL=Ceiling[Log 2(M)]  (32)where M is the product of the relatively prime numbers p₀, p₁, . . . ,p_(N−1) selected as moduli m₀, m₁, . . . , m_(N−1). In this regard, itshould be appreciated that M represents a dynamic range of a CRTarithmetic operation. The phrase “dynamic range”, as used herein, refersto a maximum possible range of outcome values of a CRT arithmeticoperation. It should also be appreciated that the CRT arithmeticoperation generates a chaotic numerical sequence with a periodicityequal to the inverse of the dynamic range M. The dynamic range requiresa Ceiling[Log 2(M)] bit precision.

According to an embodiment of the invention, M equals three quadrillionfive hundred sixty-three trillion seven hundred sixty-two billion onehundred ninety-one million fifty-nine thousand five hundred twenty-three(3,563,762,191,059,523). By substituting the value of M intomathematical equation (8), the bit length (BL) for a chaotic sequenceoutput Y expressed in a binary system representation can be calculatedas follows: BL=Ceiling[Log 2(3,563,762,191,059,523)]=52 bits. As such,the chaotic sequence output is a fifty-two (52) bit binary sequencehaving an integer value between zero (0) and three quadrillion fivehundred sixty-three trillion seven hundred sixty-two billion one hundredninety-one million fifty-nine thousand five hundred twenty-two(3,563,762,191,059,522), inclusive. Embodiments of the present inventionare not limited in this regard. For example, the chaotic sequence outputcan be a binary sequence representing a truncated portion of a valuebetween zero (0) and M−1. In such a scenario, the chaotic sequenceoutput can have a bit length less than Ceiling[Log 2(M)]. It should benoted that while truncation affects the dynamic range of the system ithas no effect on the periodicity of a generated sequence.

As should be appreciated, the above-described chaotic sequencegeneration can be iteratively performed. In such a scenario, a feedbackmechanism (e.g., a feedback loop) can be provided so that a variable “x”of a polynomial equation can be selectively defined as a solutioncomputed in a previous iteration. Mathematical equation (32) can berewritten in a general iterative form:f(x(nT)=Q(k)x³((n−1)T)+R(k)x²((n−1)T)+S(k)x((n−1)T)+C(k,L). For example,a fixed coefficient polynomial equation is selected as f(x(n·1ms))=3x³((n−1)·1 ms)+3x²((n−1)·1ms)+x((n−1)·1 ms)+8 modulo 503. n is avariable having a value defined by an iteration being performed. x has avalue allowable in a residue ring. In a first iteration, n equals one(1) and x is selected as two (2) which is allowable in a residue ring.By substituting the value of n and x into the stated polynomial equationf(x(nT)), a first solution having a value forty-six (46) is obtained. Ina second iteration, n is incremented by one and x equals the value ofthe first solution, i.e., forty-six (46) resulting in the solution 298,410 mod 503 or one hundred thirty-one (131). In a third iteration, n isagain incremented by one and x equals the value of the second solution.

Referring now to FIG. 10, there is provided a flow diagram of a method1000 for generating a chaotic sequence according to an embodiment of theinvention. As shown in FIG. 10, method 1000 begins with step 1002 andcontinues with step 1004. In step 1004, a plurality of polynomialequations f₀(x(nT)), . . . , f_(N−1)(x(nT)) are selected. The polynomialequations f₀(x(nT)), . . . , f_(N−1)(x(nT)) can be selected as the samepolynomial equation except for a different constant term or differentpolynomial equations. After step 1004, step 1006 is performed where adetermination for each polynomial equation f₀(x(nT)), . . . ,f_(N−1)(x(nT)) is made as to which combinations of RNS moduli m₀, m₁, .. . , m_(N−1) used for arithmetic operations and respective constantvalues C₀, C₁, . . . , C_(N−1) generate irreducible forms of eachpolynomial equation f₀(x(nT)), . . . , f_(N−1)(x(nT)). In step 1008, amodulus is selected for each polynomial equation f₀(x(nT)), . . . ,f_(N−1)(x(nT)) that is to be used for RNS arithmetic operations whensolving the polynomial equation f₀(x(nT)), . . . , f_(N−1)(x(nT)). Themodulus is selected from the moduli identified in step 1006. It shouldalso be appreciated that a different modulus must be selected for eachpolynomial equation f₀(x(nT)), . . . , f_(N−1)(x(nT)).

As shown in FIG. 10, method 1000 continues with a step 1010. In step1010, a constant C_(m) is selected for each polynomial equationf₀(x(nT)), . . . , f_(N−1)(x(nT)) for which a modulus is selected. Eachconstant C_(m) corresponds to the modulus selected for the respectivepolynomial equation f₀(x(nT)), . . . , f_(N−1)(x(nT)). Each constantC_(m) is selected from among the possible constant values identified instep 1206 for generating an irreducible form of the respectivepolynomial equation f₀(x(nT)), . . . , f_(N−1)(x(nT)).

After step 1010, method 1000 continues with step 1012. In step 1012, avalue for time increment T is selected. Thereafter, an initial value forthe variable x of the polynomial equations is selected. The initialvalue for the variable x can be any value allowable in a residue ring.Notably, the initial value of the variable x defines a sequence startinglocation. As such, the initial value of the variable x can define astatic offset of a chaotic sequence.

Referring again to FIG. 10, method 1000 continues with step 1016. Instep 1016, RNS arithmetic operations are used to iteratively determineRNS solutions for each of the stated polynomial equations f₀(x(nT)), . .. , f_(N−1)(x(nT)). In step 1018, a series of digits in a weightednumber system are determined based in the RNS solutions. Step 1018 caninvolve performing a mixed radix arithmetic operation or a CRTarithmetic operation using the RNS solutions to obtain a chaoticsequence output.

After completing step 1018, method 1000 continues with a decision step1020. If a chaos generator is not terminated (1020:NO), then step 1024is performed where a value of the variable “x” in each polynomialequation f₀(x(nT)), . . . , f_(N−1)(x(nT)) is set equal to the RNSsolution computed for the respective polynomial equation f₀(x(nT)), . .. , f_(N−1)(x(nT)) in step 1016. Subsequently, method 1000 returns tostep 1016. If the chaos generator is terminated (1020:YES), then step1022 is performed where method 1000 ends.

Referring now to FIG. 11, there is illustrated one embodiment of thechaos generator 618 shown in FIG. 6. Chaos generators 640, 740, 760,840, 860 are the same as or substantially similar to chaos generator618. As such, the following discussion of chaos generator 618 issufficient for understanding chaos generators 640 of FIG. 6, chaosgenerators 740, 760 of FIG. 7B, and chaos generators 840, 860 of FIG.8B.

As shown in FIG. 11, chaos generator 618 is generally comprised ofhardware and/or software configured to generate a digital chaoticsequence. Accordingly, chaos generator 618 is comprised of computingprocessors 1102 ₀, . . . , 1102 _(N−1) and a mapping processor 1104.Each computing processor 1102 ₀, . . . , 1102 _(N−1) is coupled to themapping processor 1104 by a respective data bus 1106 ₀, . . . , 1106_(N−1). As such, each computing processor 1102 ₀, . . . , 1102 _(N−1) isconfigured to communicate data to the mapping processor 1104 via arespective data bus 1106 ₀, . . . , 1106 _(N−1). The mapping processor1104 can be coupled to an external device (not shown) via a data bus1108. The external device (not shown) includes, but is not limited to, acommunications device configured to combine or modify a signal inaccordance with a chaotic sequence output.

Referring again to FIG. 11, the computing processors 1102 ₀, . . . ,1102 _(N−1) are comprised of hardware and/or software configured tosolve the polynomial equations f₀(x(nT)), . . . , f_(N−1)(x(nT)) toobtain a plurality of solutions. The polynomial equations f₀(x(nT)), . .. , f_(N−1)(x(nT)) can be irreducible polynomial equations havingchaotic properties in Galois field arithmetic. Such irreduciblepolynomial equations include, but are not limited to, irreducible cubicpolynomial equations and irreducible quadratic polynomial equations. Thepolynomial equations f₀(x(nT)), . . . , f_(N−1)(x(nT)) can also beidentical exclusive of a constant value. The constant value can beselected so that a polynomial equation f₀(x(nT)), . . . , f_(N−1)(x(nT))is irreducible for a predefined modulus. The polynomial equationsf₀(x(nT)), . . . , f_(N−1)(x(nT)) can further be selected as a constantor varying function of time.

Each of the solutions can be expressed as a unique residue number system(RNS) N-tuple representation. In this regard, it should be appreciatedthat the computing processors 1102 ₀, . . . , 1102 _(N−1) employ modulooperations to calculate a respective solution for each polynomialequation f₀(x(nT)), . . . , f_(N−1)(x(nT)) using modulo based arithmeticoperations. Each of the computing processors 1102 ₀, . . . , 1102 _(N−1)is comprised of hardware and/or software configured to utilize adifferent relatively prime number p₀, p₁, . . . , p_(N−1) as a modulim₀, m₁, . . . , m_(N−1) for modulo based arithmetic operations. Thecomputing processors 1102 ₀, . . . , 1102 _(N−1) are also comprised ofhardware and/or software configured to utilize modulus m₀, m₁, . . . ,m_(N−1) selected for each polynomial equation f₀(x(nT)), . . . ,f_(N−1)(x(nT)) so that each polynomial equation f₀(x(nT)), . . . ,f_(N−1)(x(nT)) is irreducible. The computing processors 1102 ₀, . . . ,1102 _(N−1) are further comprised of hardware and/or software configuredto utilize moduli m₀, m₁, . . . , m_(N−1) selected for each polynomialequation f₀(x(nT)), . . . , f_(N−1)(x(nT)) so that solutions iterativelycomputed via a feedback mechanism 1110 ₀, . . . , 1110 _(N−1) arechaotic. In this regard, it should be appreciated that the feedbackmechanisms 1100 ₀, . . . , 1110 _(N−1) are provided so that thesolutions for each polynomial equation f₀(x(nT)), . . . , f_(N−1)(x(nT))can be iteratively computed. Accordingly, the feedback mechanisms 1110 ₀0, . . . , 1110 _(N−1) are comprised of hardware and/or softwareconfigured to selectively define variables “x” of a polynomial equationas a solution computed in a previous iteration.

Referring again to FIG. 11, the computing processors 1102 ₀, . . . ,1102 _(N−1) are further comprised of hardware and/or software configuredto express each of the RNS residue values in a binary number systemrepresentation. In this regard, the computing processors 1102 ₀, . . . ,1102 _(N−1) can employ an RNS-to-binary conversion method. SuchRNS-to-binary conversion methods are generally known to persons havingordinary skill in the art, and therefore will not be described herein.However, it should be appreciated that any such RNS-to-binary conversionmethod can be used without limitation. It should also be appreciatedthat the residue values expressed in binary number systemrepresentations are hereinafter referred to as moduli solutions No. 1, .. . , No. N comprising the elements of an RNS N-tuple.

According to an embodiment of the invention, the computing processors1102 ₀, . . . , 1102 _(N−1) are further comprised of memory based tables(not shown) containing pre-computed residue values in a binary numbersystem representation. The address space of each memory table is atleast from zero (0) to m_(m)−1 for all m, m₀ through m_(N−1). The tableaddress is used to initiate the chaotic sequence at the start of aniteration. The invention is not limited in this regard.

Referring again to FIG. 11, the mapping processor 1104 is comprised ofhardware and/or software configured to map the moduli (RNS N-tuple)solutions No. 1, . . . , No. N to a weighted number systemrepresentation. The result is a series of digits in the weighted numbersystem based on the moduli solutions No. 1, . . . , No. N. For example,the mapping processor 1104 can be comprised of hardware and/or softwareconfigured to determine the series of digits in the weighted numbersystem based on the RNS residue values using a Chinese Remainder Theoremprocess. In this regard, it will be appreciated by those having ordinaryskill in the art that the mapping processor 1104 is comprised ofhardware and/or software configured to identify a number in the weightednumber system that is defined by the moduli solutions No. 1, . . . , No.N.

According to an aspect of the invention, the mapping processor 1104 canbe comprised of hardware and/or software configured to identify atruncated portion of a number in the weighted number system that isdefined by the moduli solutions No. 1, . . . , No. N. For example,mapping processor 1104 can be comprised of hardware and/or softwareconfigured to select the truncated portion to include any seriallyarranged set of digits of the number in the weighted number system.Mapping processor 1104 can also include hardware and/or softwareconfigured to select the truncated portion to be exclusive of a mostsignificant digit when all possible weighted numbers represented by Pbits are not mapped, i.e., when M−1<2^(P). P is a fewest number of bitsrequired to achieve a binary representation of the weighted numbers. Theinvention is not limited in this regard.

Referring again to FIG. 11, mapping processor 1104 is comprised ofhardware and/or software configured to express a chaotic sequence in abinary number system representation. In this regard, it should beappreciated that the mapping processor 1104 can employ aweighted-to-binary conversion method. Weighted-to-binary conversionmethods are generally known to persons having ordinary skill in the art,and therefore will not be described herein. However, it should beappreciated that any such weighted-to-binary conversion method can beused without limitation.

All of the apparatus, methods, and algorithms disclosed and claimedherein can be made and executed without undue experimentation in lightof the present disclosure. While the invention has been described interms of preferred embodiments, it will be apparent to those havingordinary skill in the art that variations may be applied to theapparatus, methods and sequence of steps of the method without departingfrom the concept, spirit and scope of the invention. More specifically,it will be apparent that certain components may be added to, combinedwith, or substituted for the components described herein while the sameor similar results would be achieved. All such similar substitutes andmodifications apparent to those having ordinary skill in the art aredeemed to be within the spirit, scope and concept of the invention asdefined.

We claim:
 1. A method for selectively controlling access to multipledata streams which are communicated using a shared frequency spectrumand shared spreading codes, comprising: generating a first productsignal by spreading first symbols of a first amplitude modulated signalusing a first spreading code; generating a second product signal byspreading second symbols of a complimentary amplitude modulated signalusing a second spreading code; combining said first and second productsignals to form a protected data communication signal including firstdata recoverable by at least one receiver of a plurality of receivers;and combining a global data communication signal and said protected datacommunication signal to form an output signal having a spread spectrumformat; wherein said global data communication signal is generated usinga digital modulation process and includes second data recoverable by allof said plurality of receivers.
 2. The method according to claim 1,wherein said first and second spreading codes include pseudo-randomnumber sequences.
 3. The method according to claim 1, wherein said firstand second spreading codes include digitally generated chaoticsequences.
 4. The method according to claim 1, wherein said secondspreading code is orthogonal or statistically orthogonal to said firstspreading code.
 5. The method according to claim 1, wherein said digitalmodulation process includes a phase modulation process.
 6. The methodaccording to claim 1, wherein said first and second product signals areadditively combined to produce a constant power envelope in saidprotected data communication signal.
 7. The method according to claim 1,further comprising recovering said global data communication signal at afirst receiver of said plurality of receivers by de-spreading saidoutput signal using a sum of a third spreading code and a fourthspreading code which are respectively identical to said first spreadingcode and said second spreading code.
 8. The method according to claim 7,further comprising synchronizing in time said first and third spreadingcodes, and said second and fourth spreading codes.
 9. The methodaccording to claim 7, further comprising preventing said first receiverfrom independently recovering the third spreading code or the fourthspreading code.
 10. The method according to claim 1, further comprisingrecovering said first product signal at a first receiver of saidplurality of receivers by de-spreading said output using a thirdspreading code that is identical to said first spreading code.
 11. Acommunication system configured for selectively controlling access tomultiple data streams which are communicated using a shared frequencyspectrum and shared spreading codes, comprising: a first discrete timeamplitude modulator generating a first product signal by spreading firstsymbols of a first amplitude modulated signal using a first spreadingcode; a second discrete time amplitude modulator configured forgenerating a second product signal by spreading second symbols of acomplimentary amplitude modulated signal using a second spreading code;a first combiner configured for combining said first and second productsignals to form a protected data communication signal including firstdata recoverable by at least one receiver of a plurality of receivers;and a second combiner configured for combining a global datacommunication signal and said protected data communication signal toform an output signal having a spread spectrum format; wherein saidglobal data communication signal is generated using a digital modulationprocess and includes second data recoverable by all of said plurality ofreceivers.
 12. The communication system according to claim 11, whereinsaid first and second spreading codes include pseudo-random numbersequences.
 13. The communication system according to claim 11, whereinsaid first and second spreading codes include digitally generatedchaotic sequences.
 14. The communication system according to claim 11,wherein said second spreading code is orthogonal or statisticallyorthogonal to said first spreading code.
 15. The communication systemaccording to claim 11, wherein said digital modulation process includesa phase modulation process.
 16. The communication system according toclaim 11, wherein said first combiner is further configured foradditively combining said first and second product signals to produce aconstant power envelope in said protected data communication signal. 17.The communication system according to claim 11, further comprising: atransmitter configured for transmitting said output signal to a firstreceiver of said plurality of receivers; wherein said first receiver isconfigured for recovering said global data communication signal byde-spreading said output signal using a sum of a third spreading codeand a fourth spreading code which are respectively identical to saidfirst spreading code and said second spreading code.
 18. Thecommunication system according to claim 17, wherein said first and thirdspreading codes are synchronized in time and said second and fourthspreading codes are synchronized in time.
 19. The communication systemaccording to claim 17, wherein said first receiver is prevented fromindependently recovering said third spreading code or said fourthspreading code.
 20. The communication system according to claim 11,further comprising: a transmitter configured for transmitting saidoutput signal to a first receiver of said plurality of receivers;wherein said first receiver is configured for recovering said firstproduct signal by de-spreading said output using a third spreading codethat is identical to said first spreading code.